Quantifying Information Leak Vulnerabilities

Abstract: Leakage of confidential information represents a serious security risk. Despite a number of novel, theoretical advances, it has been unclear if and how quantitative approaches to measuring leakage of confidential information could be applied to substantial, real-world programs. This is mostly due to the high complexity of computing precise leakage quantities. In this paper, we introduce a technique which makes it possible to decide if a program conforms to a quantitative policy which scales to large state-spaces with the help of bounded model checking. Our technique is applied to a number of officially reported information leak vulnerabilities in the Linux Kernel. Additionally, we also analysed authentication routines in the Secure Remote Password suite and of a Internet Message Support Protocol implementation. Our technique shows when there is unacceptable leakage; the same technique is also used to verify, for the first time, that the applied software patches indeed plug the information leaks. This is the first demonstration of quantitative information flow addressing security concerns of real-world industrial programs.


End-Host Distribution in Application-Layer Multicast: Main Issues and Solutions

Abstract: Application-layer multicast implements the multicast functionality at the application layer. The main goal of application-layer multicast is to construct and maintain efficient distribution structures between end-hosts. In this paper we focus on the implementation of an application-layer multicast distribution algorithm. We observe that the total time required to measure network latency over TCP is influenced dramatically by the TCP connection time. We argue that end-host distribution is not only influenced by the quality of network links but also by the time required to make connections between nodes. We provide several solutions to decrease the total end-host distribution time.


An axiomatic formalization of bounded rationality based on a utility-information equivalence

Abstract: Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that considers resource costs. Agents are formalized as probability measures over input-output streams. We postulate that any such probability measure can be assigned a corresponding conjugate utility function based on three axioms: utilities should be real-valued, additive and monotonic mappings of probabilities. We show that these axioms enforce a unique conversion law between utility and probability (and thereby, information). Moreover, we show that this relation can be characterized as a variational principle: given a utility function, its conjugate probability measure maximizes a free utility functional. Transformations of probability measures can then be formalized as a change in free utility due to the addition of new constraints expressed by a target utility function. Accordingly, one obtains a criterion to choose a probability measure that trades off the maximization of a target utility function and the cost of the deviation from a reference distribution. We show that optimal control, adaptive estimation and adaptive control problems can be solved this way in a resource-efficient way. When resource costs are ignored, the MEU principle is recovered. Our formalization might thus provide a principled approach to bounded rationality that establishes a close link to information theory.


Analysis of Spatio-Temporal Preferences and Encounter Statistics for DTN Performance

Abstract: Spatio-temporal preferences and encounter statistics provide realistic measures to understand mobile user's behavioral preferences and transfer opportunities in Delay Tolerant Networks (DTNs). The time dependent behavior and periodic reappearances at specific locations can approximate future online presence while encounter statistics can aid to forward the routing decisions. It is theoretically shown that such characteristics heavily affect the performance of routing protocols. Therefore, mobility models demonstrating such characteristics are also expected to show identical routing performance. However, we argue models despite capturing these properties deviate from their expected routing performance. We use realistic traces to validate this observation on two mobility models. Our empirical results for epidemic routing show those models' largely differ (delay 67% & reachability 79%) from the observed values. This in-turn call for two important activities: (i) Analogous to routing, explore structural properties on a Global scale (ii) Design new mobility models that capture them.


Bilateral filters: what they can and cannot do

Abstract: Nonlinear bilateral filters (BF) deliver a fine blend of computational simplicity and blur-free denoising. However, little is known about their nature, noise-suppressing properties, and optimal choices of filter parameters. Our study is meant to fill this gap-explaining the underlying mechanism of bilateral filtering and providing the methodology for optimal filter selection. Practical application to CT image denoising is discussed to illustrate our results.


Handling software upgradeability problems with MILP solvers

Abstract: Upgradeability problems are a critical issue in modern operating systems. The problem consists in finding the "best" solution according to some criteria, to install, remove or upgrade packages in a given installation. This is a difficult problem: the complexity of the upgradeability problem is NP complete and modern OS contain a huge number of packages (often more than 20 000 packages in a Linux distribution). Moreover, several optimisation criteria have to be considered, e.g., stability, memory efficiency, network efficiency. In this paper we investigate the capabilities of MILP solvers to handle this problem. We show that MILP solvers are very efficient when the resolution is based on a linear combination of the criteria. Experiments done on real benchmarks show that the best MILP solvers outperform CP solvers and that they are significantly better than Pseudo Boolean solvers.


Solving Linux Upgradeability Problems Using Boolean Optimization

Abstract: Managing the software complexity of package-based systems can be regarded as one of the main challenges in software architectures. Upgrades are required on a short time basis and systems are expected to be reliable and consistent after that. For each package in the system, a set of dependencies and a set of conflicts have to be taken into account. Although this problem is computationally hard to solve, efficient tools are required. In the best scenario, the solutions provided should also be optimal in order to better fulfill users requirements and expectations. This paper describes two different tools, both based on Boolean satisfiability (SAT), for solving Linux upgradeability problems. The problem instances used in the evaluation of these tools were mainly obtained from real environments, and are subject to two different lexicographic optimization criteria. The developed tools can provide optimal solutions for many of the instances, but a few challenges remain. Moreover, it is our understanding that this problem has many similarities with other configuration problems, and therefore the same techniques can be used in other domains.


Comparison of PBO solvers in a dependency solving domain

Abstract: Linux package managers have to deal with dependencies and conflicts of packages required to be installed by the user. As an NP-complete problem, this is a hard task to solve. In this context, several approaches have been pursued. Apt-pbo is a package manager based on the apt project that encodes the dependency solving problem as a pseudo-Boolean optimization (PBO) problem. This paper compares different PBO solvers and their effectiveness on solving the dependency solving problem.


CONFIGEN: A tool for managing configuration options

Abstract: This paper introduces CONFIGEN, a tool that helps modularizing software. CONFIGEN allows the developer to select a set of elementary components for his software through an interactive interface. Configuration files for use by C/assembly code and Makefiles are then automatically generated, and we successfully used it as a helper tool for complex system software refactoring. CONFIGEN is based on propositional logic, and its implementation faces hard theoretical problems.


Model Counting in Product Configuration

Abstract: We describe how to use propositional model counting for a quantitative analysis of product configuration data. Our approach computes valuable meta information such as the total number of valid configurations or the relative frequency of components. This information can be used to assess the severity of documentation errors or to measure documentation quality. As an application example we show how we apply these methods to product documentation formulas of the Mercedes-Benz line of vehicles. In order to process these large formulas we developed and implemented a new model counter for non-CNF formulas. Our model counter can process formulas, whose CNF representations could not be processed up till now.


Registration of Brain Images using Fast Walsh Hadamard Transform

Abstract: A lot of image registration techniques have been developed with great significance for data analysis in medicine, astrophotography, satellite imaging and few other areas. This work proposes a method for medical image registration using Fast Walsh Hadamard transform. This algorithm registers images of the same or different modalities. Each image bit is lengthened in terms of Fast Walsh Hadamard basis functions. Each basis function is a notion of determining various aspects of local structure, e.g., horizontal edge, corner, etc. These coefficients are normalized and used as numerals in a chosen number system which allows one to form a unique number for each type of local structure. The experimental results show that Fast Walsh Hadamard transform accomplished better results than the conventional Walsh transform in the time domain. Also Fast Walsh Hadamard transform is more reliable in medical image registration consuming less time.


Simple Gradecast Based Algorithms

Abstract: Gradecast is a simple three-round algorithm presented by Feldman and Micali. The current work presents a very simple algorithm that utilized Gradecast to achieve Byzantine agreement. Two small variations of the presented algorithm lead to improved algorithms for solving the Approximate agreement problem and the Multi-consensus problem. An optimal approximate agreement algorithm was presented by Fekete, which supports up to 1/4 n Byzantine nodes and has message complexity of O(n^k), where n is the number of nodes and k is the number of rounds. Our solution to the approximate agreement problem is optimal, simple and reduces the message complexity to O(k * n^3), while supporting up to 1/3 n Byzantine nodes. Multi consensus was first presented by Bar-Noy et al. It consists of consecutive executions of l Byzantine consensuses. Bar-Noy et al., show an optimal amortized solution to this problem, assuming that all nodes start each consensus instance at the same time, a property that cannot be guaranteed with early stopping. Our solution is simpler, preserves round complexity optimality, allows early stopping and does not require synchronized starts of the consensus instances.


Compositional closure for Bayes Risk in probabilistic noninterference

Abstract: We give a sequential model for noninterference security including probability (but not demonic choice), thus supporting reasoning about the likelihood that high-security values might be revealed by observations of low-security activity. Our novel methodological contribution is the definition of a refinement order and its use to compare security measures between specifications and (their supposed) implementations. This contrasts with the more common practice of evaluating the security of individual programs in isolation. The appropriateness of our model and order is supported by our showing that our refinement order is the greatest compositional relation --the compositional closure-- with respect to our semantics and an "elementary" order based on Bayes Risk --- a security measure already in widespread use. We also relate refinement to other measures such as Shannon Entropy. By applying the approach to a non-trivial example, the anonymous-majority Three-Judges protocol, we demonstrate by example that correctness arguments can be simplified by the sort of layered developments --through levels of increasing detail-- that are allowed and encouraged by compositional semantics.


Learning Read-Once Functions Using Subcube Identity Queries

Abstract: We consider the problem of exact identification for read-once functions over arbitrary Boolean bases. We introduce a new type of queries (subcube identity ones), discuss its connection to previously known ones, and study the complexity of the problem in question. Besides these new queries, learning algorithms are allowed to use classic membership ones. We present a technique of modeling an equivalence query with a polynomial number of membership and subcube identity ones, thus establishing (under certain conditions) a polynomial upper bound on the complexity of the problem. We show that in some circumstances, though, equivalence queries cannot be modeled with a polynomial number of subcube identity and membership ones. We construct an example of an infinite Boolean basis with an exponential lower bound on the number of membership and subcube identity queries required for exact identification. We prove that for any finite subset of this basis, the problem remains polynomial.


On the Power of Impersonation Attacks

Abstract: In this paper we consider a synchronous message passing system in which in every round an external adversary is able to send each processor up to k messages with falsified sender identities and arbitrary content. It is formally shown that this impersonation model is slightly stronger than the asynchronous message passing model with crash failures. In particular, we prove that (k+1)-set agreement can be solved in this model, while k-set agreement is impossible, for any k>=1. The different strength of the asynchronous and impersonation models is exhibited by the order preserving renaming problem, for which an algorithm with n+k target namespace exists in the impersonation model, while an exponentially larger namespace is required in case of asynchrony.


Collision Codes: Decoding Superimposed BPSK Modulated Wireless Transmissions

Abstract: The introduction of physical layer network coding gives rise to the concept of turning a collision of transmissions on a wireless channel useful. In the idea of physical layer network coding, two synchronized simultaneous packet transmissions are carefully encoded such that the superimposed transmission can be decoded to produce a packet which is identical to the bitwise binary sum of the two transmitted packets. This paper explores the decoding of superimposed transmission resulted by multiple synchronized simultaneous transmissions. We devise a coding scheme that achieves the identification of individual transmission from the synchronized superimposed transmission. A mathematical proof for the existence of such a coding scheme is given.


Narrow sieves for parameterized paths and packings

Abstract: We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in time exponential only in the parameter (k, p, q) and using polynomial space; the constant bases of the exponentials are significantly smaller than in previous works. For example, for the k-path problem the improvement is from 2 to 1.66. We also show how to detect if a d-regular graph admits an edge coloring with $d$ colors in time within a polynomial factor of O(2^{(d-1)n/2}). Our techniques build upon and generalize some recently published ideas by I. Koutis (ICALP 2009), R. Williams (IPL 2009), and A. Bj\"orklund (STACS 2010, FOCS 2010).


Using CSP To Improve Deterministic 3-SAT

Abstract: We show how one can use certain deterministic algorithms for higher-value constraint satisfaction problems (CSPs) to speed up deterministic local search for 3-SAT. This way, we improve the deterministic worst-case running time for 3-SAT to O(1.439^n).


A Jamming-Resistant MAC Protocol for Multi-Hop Wireless Networks

Abstract: This paper presents a simple local medium access control protocol, called \textsc{Jade}, for multi-hop wireless networks with a single channel that is provably robust against adaptive adversarial jamming. The wireless network is modeled as a unit disk graph on a set of nodes distributed arbitrarily in the plane. In addition to these nodes, there are adversarial jammers that know the protocol and its entire history and that are allowed to jam the wireless channel at any node for an arbitrary $(1-\epsilon)$-fraction of the time steps, where $0<\epsilon<1$ is an arbitrary constant. We assume that the nodes cannot distinguish between jammed transmissions and collisions of regular messages. Nevertheless, we show that \textsc{Jade} achieves an asymptotically optimal throughput if there is a sufficiently dense distribution of nodes.


Inter-Sensing Time Optimization in Cognitive Radio Networks

Abstract: We consider a set of primary channels that operate in an unslotted fashion, switching activity at random times. A secondary user senses the primary channels searching for transmission opportunities. If a channel is sensed to be free, the secondary terminal transmits, and if sensed to be busy, the secondary transmitter remains silent.We solve the problem of determining the optimal time after which a primary channel needs to be sensed again depending on the sensing outcome. The objective is to find the inter-sensing times such that the mean secondary throughput is maximized while imposing a constraint over the maximum tolerable interference inflicted on the primary network. Our numerical results show that by optimizing the sensing-dependent inter-sensing times, our proposed scheme reduces the impact of sensing errors caused by false alarm and misdetection and outperforms the case of a single sensing period.


Minimum Sum Dipolar Spanning Tree in R^3

Abstract: In this paper we consider finding a geometric minimum-sum dipolar spanning tree in R^3, and present an algorithm that takes O(n^2 log^2 n) time using O(n^2) space, thus almost matching the best known results for the planar case. Our solution uses an interesting result related to the complexity of the common intersection of n balls in R^3, of possible different radii, that are all tangent to a given point p. The problem has applications in communication networks, when the goal is to minimize the distance between two hubs or servers as well as the distance from any node in the network to the closer of the two hubs. The approach used in this paper also provides a solution to the discrete 2-center problem in R^3 within the same time and space bounds.


Submodularity on a tree: Unifying $L^\natural$-convex and bisubmodular functions

Abstract: We introduce a new class of functions that can be minimized in polynomial time in the value oracle model. These are functions $f$ satisfying $f(x)+f(y)\ge f(x \sqcap y)+f(x \sqcup y)$ where the domain of each variable $x_i$ corresponds to nodes of a rooted binary tree, and operations $\sqcap,\sqcup$ are defined with respect to this tree. Special cases include previously studied $L^\natural$-convex and bisubmodular functions, which can be obtained with particular choices of trees. We present a polynomial-time algorithm for minimizing functions in the new class. It combines Murota's steepest descent algorithm for $L^\natural$-convex functions with bisubmodular minimization algorithms.


An Alternative Approach of Steganography using Reference Image

Abstract: This paper is to create a practical steganographic implementation for 4-bit images.The proposed technique converts 4 bit image into 4 shaded Gray Scale image. This image will be act as reference image to hide the text. Using this grey scale reference image any text can be hidden. Single character of a text can be represented by 8-bit. The 8-bit character can be split into 4X2 bit information. If the reference image and the data file are transmitted through network separately, we can achieve the effect of Steganography. Here the image is not at all distorted because said image is only used for referencing. Any huge mount of text material can be hidden using a very small image. Decipher the text is not possible intercepting the image or data file separately. So, it is more secure.


Privacy-Preserving Access of Outsourced Data via Oblivious RAM Simulation

Abstract: Suppose a client, Alice, has outsourced her data to an external storage provider, Bob, because he has capacity for her massive data set, of size n, whereas her private storage is much smaller--say, of size O(n^{1/r}), for some constant r > 1. Alice trusts Bob to maintain her data, but she would like to keep its contents private. She can encrypt her data, of course, but she also wishes to keep her access patterns hidden from Bob as well. We describe schemes for the oblivious RAM simulation problem with a small logarithmic or polylogarithmic amortized increase in access times, with a very high probability of success, while keeping the external storage to be of size O(n). To achieve this, our algorithmic contributions include a parallel MapReduce cuckoo-hashing algorithm and an external-memory dataoblivious sorting algorithm.


A Dense Hierarchy of Sublinear Time Approximation Schemes for Bin Packing

Abstract: The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes $a_1,..., a_n$ in $(0,1]$. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized $O({n(\log n)(\log\log n)\over \sum_{i=1}^n a_i}+({1\over \epsilon})^{O({1\over\epsilon})})$ time $(1+\epsilon)$-approximation scheme for the bin packing problem. We show that every randomized algorithm with uniform random sampling needs $\Omega({n\over \sum_{i=1}^n a_i})$ time to give an $(1+\epsilon)$-approximation. For each function $s(n): N\rightarrow N$, define $\sum(s(n))$ to be the set of all bin packing problems with the sum of item sizes equal to $s(n)$. For a constant $b\in (0,1)$, every problem in $\sum(n^{b})$ has an $O(n^{1-b}(\log n)(\log\log n)+({1\over \epsilon})^{O({1\over\epsilon})})$ time $(1+\epsilon)$-approximation for an arbitrary constant $\epsilon$. On the other hand, there is no $o(n^{1-b})$ time $(1+\epsilon)$-approximation scheme for the bin packing problems in $\sum(n^{b})$ for some constant $\epsilon>0$.


MalStone: Towards A Benchmark for Analytics on Large Data Clouds

Abstract: Developing data mining algorithms that are suitable for cloud computing platforms is currently an active area of research, as is developing cloud computing platforms appropriate for data mining. Currently, the most common benchmark for cloud computing is the Terasort (and related) benchmarks. Although the Terasort Benchmark is quite useful, it was not designed for data mining per se. In this paper, we introduce a benchmark called MalStone that is specifically designed to measure the performance of cloud computing middleware that supports the type of data intensive computing common when building data mining models. We also introduce MalGen, which is a utility for generating data on clouds that can be used with MalStone.


Network Traffic Anomalies Detection and Identification with Flow Monitoring

Abstract: Network management and security is currently one of the most vibrant research areas, among which, research on detecting and identifying anomalies has attracted a lot of interest. Researchers are still struggling to find an effective and lightweight method for anomaly detection purpose. In this paper, we propose a simple, robust method that detects network anomalous traffic data based on flow monitoring. Our method works based on monitoring the four predefined metrics that capture the flow statistics of the network. In order to prove the power of the new method, we did build an application that detects network anomalies using our method. And the result of the experiments proves that by using the four simple metrics from the flow data, we do not only effectively detect but can also identify the network traffic anomalies.


Context Awareness Framework Based on Contextual Graph

Abstract: Nowadays computing becomes increasingly mobile and pervasive. One of the important steps in pervasive computing is context-awareness. Context-aware pervasive systems rely on information about the context and user preferences to adapt their behavior. However, context-aware applications do not always behave as user's desire, and can cause users to feel dissatisfied with unexpected actions. To solve these problems, context-aware systems must provide mechanisms to adapt automatically when the context changes significantly. The interesting characteristic of context is its own behaviors which depend on various aspects of the surrounding contexts. This paper uses contextual graphs to solve the problem "the mutual relationships among the contexts". We describe the most relevant work in this area, as well as ongoing research on developing context-aware system for ubiquitous computing based on contextual graph. The usage of contextual graph in context-awareness is expected to make it effective for developers to develop various applications with the need of context reasoning.


Network Anomaly Detection: Flow-based or Packet-based Approach?

Abstract: One of the most critical tasks for network administrator is to ensure system uptime and availability. For the network security, anomaly detection systems, along with firewalls and intrusion prevention systems are the must-have tools. So far in the field of network anomaly detection, people are working on two different approaches. One is flow-based; usually rely on network elements to make so-called flow information available for analysis. The second approach is packet-based; which directly analyzes the data packet information for the detection of anomalies. This paper describes the main differences between the two approaches through an in-depth analysis. We try to answer the question of when and why an approach is better than the other. The answer is critical for network administrators to make their choices in deploying a defending system, securing the network and ensuring business continuity.


Application of Data Mining to Network Intrusion Detection: Classifier Selection Model

Abstract: As network attacks have increased in number and severity over the past few years, intrusion detection system (IDS) is increasingly becoming a critical component to secure the network. Due to large volumes of security audit data as well as complex and dynamic properties of intrusion behaviors, optimizing performance of IDS becomes an important open problem that is receiving more and more attention from the research community. The uncertainty to explore if certain algorithms perform better for certain attack classes constitutes the motivation for the reported herein. In this paper, we evaluate performance of a comprehensive set of classifier algorithms using KDD99 dataset. Based on evaluation results, best algorithms for each attack category is chosen and two classifier algorithm selection models are proposed. The simulation result comparison indicates that noticeable performance improvement and real-time intrusion detection can be achieved as we apply the proposed models to detect different kinds of network attacks.


From Pathwidth to Connected Pathwidth

Abstract: It is proven that the connected pathwidth of any graph $G$ is at most $2\cdot\pw(G)+1$, where $\pw(G)$ is the pathwidth of $G$. The method is constructive, i.e. it yields an efficient algorithm that for a given path decomposition of width $k$ computes a connected path decomposition of width at most $2k+1$. The running time of the algorithm is $O(dk^2)$, where $d$ is the number of `bags' in the input path decomposition. The motivation for studying connected path decompositions comes from the connection between the pathwidth and the search number of a graph. One of the advantages of the above bound for connected pathwidth is an inequality $\csn(G)\leq 2\sn(G)+3$, where $\csn(G)$ and $\sn(G)$ are the connected search number and the search number of $G$. Moreover, the algorithm presented in this work can be used to convert a given search strategy using $k$ searchers into a (monotone) connected one using $2k+3$ searchers and starting at an arbitrary homebase.


How to Maximize User Satisfaction Degree in Multi-service IP Networks

Abstract: Bandwidth allocation is a fundamental problem in communication networks. With current network moving towards the Future Internet model, the problem is further intensified as network traffic demanding far from exceeds network bandwidth capability. Maintaining a certain user satisfaction degree therefore becomes a challenge research topic. In this paper, we deal with the problem by proposing BASMIN, a novel bandwidth allocation scheme that aims to maximize network user's happiness. We also defined a new metric for evaluating network user satisfaction degree: network worth. A three-step evaluation process is then conducted to compare BASMIN efficiency with other three popular bandwidth allocation schemes. Throughout the tests, we experienced BASMIN's advantages over the others; we even found out that one of the most widely used bandwidth allocation schemes, in fact, is not effective at all.


Online Vertex-Weighted Bipartite Matching and Single-bid Budgeted Allocations

Abstract: We study the following vertex-weighted online bipartite matching problem: $G(U, V, E)$ is a bipartite graph. The vertices in $U$ have weights and are known ahead of time, while the vertices in $V$ arrive online in an arbitrary order and have to be matched upon arrival. The goal is to maximize the sum of weights of the matched vertices in $U$. When all the weights are equal, this reduces to the classic \emph{online bipartite matching} problem for which Karp, Vazirani and Vazirani gave an optimal $\left(1-\frac{1}{e}\right)$-competitive algorithm in their seminal work~\cite{KVV90}. Our main result is an optimal $\left(1-\frac{1}{e}\right)$-competitive randomized algorithm for general vertex weights. We use \emph{random perturbations} of weights by appropriately chosen multiplicative factors. Our solution constitutes the first known generalization of the algorithm in~\cite{KVV90} in this model and provides new insights into the role of randomization in online allocation problems. It also effectively solves the problem of \emph{online budgeted allocations} \cite{MSVV05} in the case when an agent makes the same bid for any desired item, even if the bid is comparable to his budget - complementing the results of \cite{MSVV05, BJN07} which apply when the bids are much smaller than the budgets.


Context Ontology Implementation for Smart Home

Abstract: Context awareness is one of the important fields in ubiquitous computing. Smart Home, a specific instance of ubiquitous computing, provides every family with opportunities to enjoy the power of hi-tech home living. Discovering that relationship among user, activity and context data in home environment is semantic, therefore, we apply ontology to model these relationships and then reason them as the semantic information. In this paper, we present the realization of smart home's context-aware system based on ontology. We discuss the current challenges in realizing the ontology context base. These challenges can be listed as collecting context information from heterogeneous sources, such as devices, agents, sensors into ontology, ontology management, ontology querying, and the issue related to environment database explosion.


Development of a Context Aware Virtual Smart Home Simulator

Abstract: Context awareness is the most important research area in ubiquitous computing. In particular, for smart home, context awareness attempts to bring the best services to the home habitants. However, the implementation in the real environment is not easy and takes a long time from building the scratch. Thus, to support the implementation in the real smart home, it is necessary to demonstrate that thing can be done in the simulator in which context information can be created by virtual sensors instead of physical sensors. In this paper, we propose ISS, an Interactive Smart home Simulator system aiming at controlling and simulating the behavior of an intelligent house. The developed system aims to provide architects, designers a simulation and useful tool for understanding the interaction between environment, people and the impact of embedded and pervasive technology on in daily life. In this research, the smart house is considered as an environment made up of independent and distributed devices interacting to support user's goals and tasks. Therefore, by using ISS, the developer can realize the relationship among virtual home space, surrounded environment, use and home appliances.


A note on sample complexity of learning binary output neural networks under fixed input distributions

Abstract: We show that the learning sample complexity of a sigmoidal neural network constructed by Sontag (1992) required to achieve a given misclassification error under a fixed purely atomic distribution can grow arbitrarily fast: for any prescribed rate of growth there is an input distribution having this rate as the sample complexity, and the bound is asymptotically tight. The rate can be superexponential, a non-recursive function, etc. We further observe that Sontag's ANN is not Glivenko-Cantelli under any input distribution having a non-atomic part.


Minimisation of Deterministic Parity and Buchi Automata and Relative Minimisation of Deterministic Finite Automata

Abstract: In this report we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic Buchi, Co-Buchi, and parity automata play a similar role in the recognition of \omega-regular languages. While it is well known that the minimisation of deterministic finite and weak automata is cheap, the complexity of minimising deterministic Buchi and parity automata has remained an open challenge. We establish the NP-completeness of these problems. A second contribution of this report is the introduction of relaxed minimisation of deterministic finite automata. Like hyper-minimisation, relaxed minimisation allows for some changes in the language of the automaton: We seek a smallest automaton that, when used as a monitor, provides a wrong answer only a bounded number of times in any run of a system. We argue that minimisation of finite automata, hyper-minimisation, relaxed minimisation, and the minimisation of deterministic Buchi (or Co-Buchi) automata are operations of increasing reduction power, as the respective equivalence relations on automata become coarser from left to right. When we allow for minor changes in the language, relaxed minimisation can therefore be considered as a more powerful minimisation technique than hyper-minimisation from the perspective of finite automata. From the perspective of Buchi and Co-Buchi automata, we gain a cheap algorithm for state-space reduction that also turns out to be beneficial for further heuristic or exhaustive state-space reductions put on top of it.


Top-K Color Queries for Document Retrieval

Abstract: In this paper we describe a new efficient (in fact optimal) data structure for the {\em top-$K$ color problem}. Each element of an array $A$ is assigned a color $c$ with priority $p(c)$. For a query range $[a,b]$ and a value $K$, we have to report $K$ colors with the highest priorities among all colors that occur in $A[a..b]$, sorted in reverse order by their priorities. We show that such queries can be answered in $O(K)$ time using an $O(N\log \sigma)$ bits data structure, where $N$ is the number of elements in the array and $\sigma$ is the number of colors. Thus our data structure is asymptotically optimal with respect to the worst-case query time and space. As an immediate application of our results, we obtain optimal time solutions for several document retrieval problems. The method of the paper could be also of independent interest.


On independent sets in random graphs

Abstract: The independence number of a sparse random graph G(n,m) of average degree d=2m/n is well-known to be \alpha(G(n,m))~2n ln(d)/d with high probability. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size (1+o(1)) n ln(d)/d, i.e. half the maximum size. Yet in spite of 30 years of extensive research no efficient algorithm has emerged to produce an independent set with (1+c)n ln(d)/d, for any fixed c>0. In this paper we prove that the combinatorial structure of the independent set problem in random graphs undergoes a phase transition as the size k of the independent sets passes the point k nln(d)/d. Roughly speaking, we prove that independent sets of size k>(1+c)n ln(d)/d form an intricately ragged landscape, in which local search algorithms are bound to get stuck. We illustrate this phenomenon by providing an exponential lower bound for the Metropolis process, a Markov chain for sampling independents sets.


A Flexible Patch-Based Lattice Boltzmann Parallelization Approach for Heterogeneous GPU-CPU Clusters

Abstract: Sustaining a large fraction of single GPU performance in parallel computations is considered to be the major problem of GPU-based clusters. In this article, this topic is addressed in the context of a lattice Boltzmann flow solver that is integrated in the WaLBerla software framework. We propose a multi-GPU implementation using a block-structured MPI parallelization, suitable for load balancing and heterogeneous computations on CPUs and GPUs. The overhead required for multi-GPU simulations is discussed in detail and it is demonstrated that the kernel performance can be sustained to a large extent. With our GPU implementation, we achieve nearly perfect weak scalability on InfiniBand clusters. However, in strong scaling scenarios multi-GPUs make less efficient use of the hardware than IBM BG/P and x86 clusters. Hence, a cost analysis must determine the best course of action for a particular simulation task. Additionally, weak scaling results of heterogeneous simulations conducted on CPUs and GPUs simultaneously are presented using clusters equipped with varying node configurations.


Multi-environment model estimation for motility analysis of Caenorhabditis Elegans

Abstract: The nematode Caenorhabditis elegans is a well-known model organism used to investigate fundamental questions in biology. Motility assays of this small roundworm are designed to study the relationships between genes and behavior. Commonly, motility analysis is used to classify nematode movements and characterize them quantitatively. Over the past years, C. elegans' motility has been studied across a wide range of environments, including crawling on substrates, swimming in fluids, and locomoting through microfluidic substrates. However, each environment often requires customized image processing tools relying on heuristic parameter tuning. In the present study, we propose a novel Multi-Environment Model Estimation (MEME) framework for automated image segmentation that is versatile across various environments. The MEME platform is constructed around the concept of Mixture of Gaussian (MOG) models, where statistical models for both the background environment and the nematode appearance are explicitly learned and used to accurately segment a target nematode. Our method is designed to simplify the burden often imposed on users; here, only a single image which includes a nematode in its environment must be provided for model learning. In addition, our platform enables the extraction of nematode `skeletons' for straightforward motility quantification. We test our algorithm on various locomotive environments and compare performances with an intensity-based thresholding method. Overall, MEME outperforms the threshold-based approach for the overwhelming majority of cases examined. Ultimately, MEME provides researchers with an attractive platform for C. elegans' segmentation and `skeletonizing' across a wide range of motility assays.


Improved RANSAC performance using simple, iterative minimal-set solvers

Abstract: RANSAC is a popular technique for estimating model parameters in the presence of outliers. The best speed is achieved when the minimum possible number of points is used to estimate hypotheses for the model. Many useful problems can be represented using polynomial constraints (for instance, the determinant of a fundamental matrix must be zero) and so have a number of solutions which are consistent with a minimal set. A considerable amount of effort has been expended on finding the constraints of such problems, and these often require the solution of systems of polynomial equations. We show that better performance can be achieved by using a simple optimization based approach on minimal sets. For a given minimal set, the optimization approach is not guaranteed to converge to the correct solution. However, when used within RANSAC the greater speed and numerical stability results in better performance overall, and much simpler algorithms. We also show that by selecting more than the minimal number of points and using robust optimization can yield better results for very noisy by reducing the number of trials required. The increased speed of our method demonstrated with experiments on essential matrix estimation.


Intrusions into Privacy in Video Chat Environments: Attacks and Countermeasures

Abstract: Video chat systems such as Chatroulette have become increasingly popular as a way to meet and converse one-on-one via video and audio with other users online in an open and interactive manner. At the same time, security and privacy concerns inherent in such communication have been little explored. This paper presents one of the first investigations of the privacy threats found in such video chat systems, identifying three such threats, namely de-anonymization attacks, phishing attacks, and man-in-the-middle attacks. The paper further describes countermeasures against each of these attacks.


Flows in One-Crossing-Minor-Free Graphs

Abstract: We study the maximum flow problem in directed H-minor-free graphs where H can be drawn in the plane with one crossing. If a structural decomposition of the graph as a clique-sum of planar graphs and graphs of constant complexity is given, we show that a maximum flow can be computed in O(n log n) time. In particular, maximum flows in directed K_{3,3}-minor-free graphs and directed K_5-minor-free graphs can be computed in O(n log n) time without additional assumptions.


Optimal Pricing in Social Networks with Incomplete Information

Abstract: In revenue maximization of selling a digital product in a social network, the utility of an agent is often considered to have two parts: a private valuation, and linearly additive influences from other agents. We study the incomplete information case where agents know a common distribution about others' private valuations, and make decisions simultaneously. The "rational behavior" of agents in this case is captured by the well-known Bayesian Nash equilibrium. Two challenging questions arise: how to compute an equilibrium and how to optimize a pricing strategy accordingly to maximize the revenue assuming agents follow the equilibrium? In this paper, we mainly focus on the natural model where the private valuation of each agent is sampled from a uniform distribution, which turns out to be already challenging. Our main result is a polynomial-time algorithm that can exactly compute the equilibrium and the optimal price, when pairwise influences are non-negative. If negative influences are allowed, computing any equilibrium even approximately is PPAD-hard. Our algorithm can also be used to design an FPTAS for optimizing discriminative price profile.


An Optimal Lower Bound for Buffer Management in Multi-Queue Switches

Abstract: In the online packet buffering problem (also known as the unweighted FIFO variant of buffer management), we focus on a single network packet switching device with several input ports and one output port. This device forwards unit-size, unit-value packets from input ports to the output port. Buffers attached to input ports may accumulate incoming packets for later transmission; if they cannot accommodate all incoming packets, their excess is lost. A packet buffering algorithm has to choose from which buffers to transmit packets in order to minimize the number of lost packets and thus maximize the throughput. We present a tight lower bound of e/(e-1) ~ 1.582 on the competitive ratio of the throughput maximization, which holds even for fractional or randomized algorithms. This improves the previously best known lower bound of 1.4659 and matches the performance of the algorithm Random Schedule. Our result contradicts the claimed performance of the algorithm Random Permutation; we point out a flaw in its original analysis.


Stability Analysis of GI/G/c/K Retrial Queue with Constant Retrial Rate

Abstract: We consider a GI/G/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has $c$ identical servers and can accommodate the maximal number of $K$ jobs. If a newly arriving job finds the full primary queue, it joins the orbit. The original primary jobs arrive to the system according to a renewal process. The jobs have general i.i.d. service times. A job in front of the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the orbit queue length. Telephone exchange systems, Medium Access Protocols and short TCP transfers are just some applications of the proposed queueing system. For this system we establish minimal sufficient stability conditions. Our model is very general. In addition, to the known particular cases (e.g., M/G/1/1 or M/M/c/c systems), the proposed model covers as particular cases the deterministic service model and the Erlang model with constant retrial rate. The latter particular cases have not been considered in the past. The obtained stability conditions have clear probabilistic interpretation.


An ICT based solution to make mines safer

Abstract: Concern for the human security inside mines is as old as the mining itself. However, ICT (Information and communication technologies), which has impacted human life in so many ways has not been much used for making mines safer. We propose a method that has been practically implemented which can enhance mine safety enormously. It is based on integration of wireless sensor network with an external network through a gateway.


A Fast Algorithm for Three-Dimensional Layers of Maxima Problem

Abstract: We show that the three-dimensional layers-of-maxima problem can be solved in $o(n\log n)$ time in the word RAM model. Our algorithm runs in $O(n(\log \log n)^3)$ deterministic time or $O(n(\log\log n)^2)$ expected time and uses O(n) space. We also describe an algorithm that uses optimal O(n) space and solves the three-dimensional layers-of-maxima problem in $O(n\log n)$ time in the pointer machine model.


Infectious Random Walks

Abstract: We study the dynamics of information (or virus) dissemination by $m$ mobile agents performing independent random walks on an $n$-node grid. We formulate our results in terms of two scenarios: broadcasting and gossiping. In the broadcasting scenario, the mobile agents are initially placed uniformly at random among the grid nodes. At time 0, one agent is informed of a rumor and starts a random walk. When an informed agent meets an uninformed agent, the latter becomes informed and starts a new random walk. We study the broadcasting time of the system, that is, the time it takes for all agents to know the rumor. In the gossiping scenario, each agent is given a distinct rumor at time 0 and all agents start random walks. When two agents meet, they share all rumors they are aware of. We study the gossiping time of the system, that is, the time it takes for all agents to know all rumors. We prove that both the broadcasting and the gossiping times are $\tilde\Theta(n/\sqrt{m})$ w.h.p., thus achieving a tight characterization up to logarithmic factors. Previous results for the grid provided bounds which were weaker and only concerned average times. In the context of virus infection, a corollary of our results is that static and dynamically moving agents are infected at about the same speed.


A Constant-Factor Approximation for Wireless Capacity Maximization with Power Control in the SINR Model

Abstract: In modern wireless networks, devices are able to set the power for each transmission carried out. Experimental but also theoretical results indicate that such power control can improve the network capacity significantly. We study this problem in the physical interference model using SINR constraints. In the SINR capacity maximization problem, we are given n pairs of senders and receivers, located in a metric space (usually a so-called fading metric). The algorithm shall select a subset of these pairs and choose a power level for each of them with the objective of maximizing the number of simultaneous communications. This is, the selected pairs have to satisfy the SINR constraints with respect to the chosen powers. We present the first algorithm achieving a constant-factor approximation in fading metrics. The best previous results depend on further network parameters such as the ratio of the maximum and the minimum distance between a sender and its receiver. Expressed only in terms of n, they are (trivial) Omega(n) approximations. Our algorithm still achieves an O(log n) approximation if we only assume to have a general metric space rather than a fading metric. Furthermore, by using standard techniques the algorithm can also be used in single-hop and multi-hop scheduling scenarios. Here, we also get polylog(n) approximations.


Scheduling for Optimal Rate Allocation in Ad Hoc Networks With Heterogeneous Delay Constraints

Abstract: This paper studies the problem of scheduling in single-hop wireless networks with real-time traffic, where every packet arrival has an associated deadline and a minimum fraction of packets must be transmitted before the end of the deadline. Using optimization and stochastic network theory we propose a framework to model the quality of service (QoS) requirements under delay constraints. The model allows for fairly general arrival models with heterogeneous constraints. The framework results in an optimal scheduling algorithm which fairly allocates data rates to all flows while meeting long-term delay demands. We also prove that under a simplified scenario our solution translates into a greedy strategy that makes optimal decisions with low complexity.


Submodular Maximization by Simulated Annealing

Abstract: We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [FOCS'07] showed a 2/5-approximation for the unconstrained problem and also proved that no approximation better than 1/2 is possible in the value oracle model. Constant-factor approximation was also given for submodular maximization subject to a matroid independence constraint (a factor of 0.309 Vondrak [FOCS'09]) and for submodular maximization subject to a matroid base constraint, provided that the fractional base packing number is at least 2 (a 1/4-approximation, Vondrak [FOCS'09]). In this paper, we propose a new algorithm for submodular maximization which is based on the idea of {\em simulated annealing}. We prove that this algorithm achieves improved approximation for two problems: a 0.41-approximation for unconstrained submodular maximization, and a 0.325-approximation for submodular maximization subject to a matroid independence constraint. On the hardness side, we show that in the value oracle model it is impossible to achieve a 0.478-approximation for submodular maximization subject to a matroid independence constraint, or a 0.394-approximation subject to a matroid base constraint in matroids with two disjoint bases. Even for the special case of cardinality constraint, we prove it is impossible to achieve a 0.491-approximation. (Previously it was conceivable that a 1/2-approximation exists for these problems.) It is still an open question whether a 1/2-approximation is possible for unconstrained submodular maximization.


Generalized Mean-payoff and Energy Games

Abstract: In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources. We prove the finite-memory determinacy of generalized energy games and show the inter-reducibility of generalized mean-payoff and energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding the existence of a winning strategy for the protagonist is NP-complete.


Online Stochastic Matching: Online Actions Based on Offline Statistics

Abstract: We consider the online stochastic matching problem proposed by Feldman et al. [FMMM09] as a model of display ad allocation. We are given a bipartite graph; one side of the graph corresponds to a fixed set of bins and the other side represents the set of possible ball types. At each time step, a ball is sampled independently from the given distribution and it needs to be matched upon its arrival to an empty bin. The goal is to maximize the number of allocations. We present an online algorithm for this problem with a competitive ratio of 0.702. Before our result, algorithms with a competitive ratio better than $1-1/e$ were known under the assumption that the expected number of arriving balls of each type is integral. A key idea of the algorithm is to collect statistics about the decisions of the optimum offline solution using Monte Carlo sampling and use those statistics to guide the decisions of the online algorithm. We also show that our algorithm achieves a competitive ratio of 0.705 when the rates are integral. On the hardness side, we prove that no online algorithm can have a competitive ratio better than 0.823 under the known distribution model (and henceforth under the permutation model). This improves upon the 5/6 hardness result proved by Goel and Mehta \cite{GM08} for the permutation model.


Can Random Coin Flips Speed Up a Computer?

Abstract: This expository essay introduces randomness and computation to a lay audience.


A Study on the Effectiveness of Different Patch Size and Shape for Eyes and Mouth Detection

Abstract: Template matching is one of the simplest methods used for eyes and mouth detection. However, it can be modified and extended to become a powerful tool. Since the patch itself plays a significant role in optimizing detection performance, a study on the influence of patch size and shape is carried out. The optimum patch size and shape is determined using the proposed method. Usually, template matching is also combined with other methods in order to improve detection accuracy. Thus, in this paper, the effectiveness of two image processing methods i.e. grayscale and Haar wavelet transform, when used with template matching are analyzed.


A Fault-Resistant Asynchronous Clock Function

Abstract: Consider an asynchronous network in a shared-memory environment consisting of n nodes. Assume that up to f of the nodes might be Byzantine (n > 12f), where the adversary is full-information and dynamic (sometimes called adaptive). In addition, the non-Byzantine nodes may undergo transient failures. Nodes advance in atomic steps, which consist of reading all registers, performing some calculation and writing to all registers. This paper contains three main contributions. First, the clock-function problem is defined, which is a generalization of the clock synchronization problem. This generalization encapsulates previous clock synchronization problem definitions while extending them to the current paper's model. Second, a randomized asynchronous self-stabilizing Byzantine tolerant clock synchronization algorithm is presented. In the construction of the clock synchronization algorithm, a building block that ensures different nodes advance at similar rates is developed. This feature is the third contribution of the paper. It is self-stabilizing and Byzantine tolerant and can be used as a building block for different algorithms that operate in an asynchronous self-stabilizing Byzantine model. The convergence time of the presented algorithm is exponential. Observe that in the asynchronous setting the best known full-information dynamic Byzantine agreement also has expected exponential convergence time, even though currently there is no known reduction between the two.


Runtime Analysis of Probabilistic Programs with Unbounded Recursion

Abstract: We study termination time and recurrence time in programs with unbounded recursion, which are either randomized or operate on some statistically quantified inputs. As the underlying formal model for such programs we use probabilistic pushdown automata (pPDA) which are equivalent to probabilistic recursive state machines. We obtain tail bounds for the distribution of termination time for pPDA. We also study the recurrence time for probabilistic recursive programs that are not supposed to terminate (such as system daemons, network servers, etc.). Typically, such programs react to certain requests generated by their environment, and hence operate in finite request-service cycles. We obtain bounds for the frequency of long request-service cycles.


A note on interval edge-colorings of graphs

Abstract: An edge-coloring of a graph $G$ with colors $1,2,\ldots,t$ is called an interval $t$-coloring if for each $i\in \{1,2,\ldots,t\}$ there is at least one edge of $G$ colored by $i$, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. In this paper we prove that if a connected graph $G$ with $n$ vertices admits an interval $t$-coloring, then $t\leq 2n-3$. We also show that if $G$ is a connected $r$-regular graph with $n$ vertices has an interval $t$-coloring and $n\geq 2r+2$, then this upper bound can be improved to $2n-5$.


A tool stack for implementing Behaviour-Driven Development in Python Language

Abstract: This paper presents a tool stack for the implementation, specification and test of software following the practices of Behavior Driven Development (BDD) in Python language. The usage of this stack highlights the specification and validation of the software's expected behavior, reducing the error rate and improving documentation. Therefore, it is possible to produce code with much less defects at both functional and unit levels, in addition to better serving to stakeholders' expectations.


Complexity of Splits Reconstruction for Low-Degree Trees

Abstract: Given a vertex-weighted tree T, the split of an edge xy in T is min{s_x(xy), s_y(xy)} where s_u(uv) is the sum of all weights of vertices that are closer to u than to v in T. Given a set of weighted vertices V and a multiset of splits S, we consider the problem of constructing a tree on V whose splits correspond to S. The problem is known to be NP-complete, even when all vertices have unit weight and the maximum vertex degree of T is required to be no more than 4. We show that the problem is strongly NP-complete when T is required to be a path, the problem is NP-complete when all vertices have unit weight and the maximum degree of T is required to be no more than 3, and it remains NP-complete when all vertices have unit weight and T is required to be a caterpillar with unbounded hair length and maximum degree at most 3. We also design polynomial time algorithms for the variant where T is required to be a path and the number of distinct vertex weights is constant, and the variant where all vertices have unit weight and T has a constant number of leaves. The latter algorithm is not only polynomial when the number of leaves, k, is a constant, but also fixed-parameter tractable when parameterized by k. Finally, we shortly discuss the problem when the vertex weights are not given but can be freely chosen by an algorithm. The considered problem is related to building libraries of chemical compounds used for drug design and discovery. In these inverse problems, the goal is to generate chemical compounds having desired structural properties, as there is a strong correlation between structural properties, such as the Wiener index, which is closely connected to the considered problem, and biological activity.


An svm multiclassifier approach to land cover mapping

Abstract: From the advent of the application of satellite imagery to land cover mapping, one of the growing areas of research interest has been in the area of image classification. Image classifiers are algorithms used to extract land cover information from satellite imagery. Most of the initial research has focussed on the development and application of algorithms to better existing and emerging classifiers. In this paper, a paradigm shift is proposed whereby a committee of classifiers is used to determine the final classification output. Two of the key components of an ensemble system are that there should be diversity among the classifiers and that there should be a mechanism through which the results are combined. In this paper, the members of the ensemble system include: Linear SVM, Gaussian SVM and Quadratic SVM. The final output was determined through a simple majority vote of the individual classifiers. From the results obtained it was observed that the final derived map generated by an ensemble system can potentially improve on the results derived from the individual classifiers making up the ensemble system. The ensemble system classification accuracy was, in this case, better than the linear and quadratic SVM result. It was however less than that of the RBF SVM. Areas for further research could focus on improving the diversity of the ensemble system used in this research.


Interactive Learning-Based Realizability for Heyting Arithmetic with EM1

Abstract: We apply to the semantics of Arithmetic the idea of ``finite approximation'' used to provide computational interpretations of Herbrand's Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for $\vee, \exists$) over a suitable structure $\StructureN$ for the language of natural numbers and maps of G\"odel's system $\SystemT$. We introduce a new Realizability semantics we call ``Interactive learning-based Realizability'', for Heyting Arithmetic plus $\EM_1$ (Excluded middle axiom restricted to $\Sigma^0_1$ formulas). Individuals of $\StructureN$ evolve with time, and realizers may ``interact'' with them, by influencing their evolution. We build our semantics over Avigad's fixed point result, but the same semantics may be defined over different constructive interpretations of classical arithmetic (Berardi and de' Liguoro use continuations). Our notion of realizability extends intuitionistic realizability and differs from it only in the atomic case: we interpret atomic realizers as ``learning agents''.


Multimode Control Attacks on Elections

Abstract: In 1992, Bartholdi, Tovey, and Trick opened the study of control attacks on elections---attempts to improve the election outcome by such actions as adding/deleting candidates or voters. That work has led to many results on how algorithms can be used to find attacks on elections and how complexity-theoretic hardness results can be used as shields against attacks. However, all the work in this line has assumed that the attacker employs just a single type of attack. In this paper, we model and study the case in which the attacker launches a multipronged (i.e., multimode) attack. We do so to more realistically capture the richness of real-life settings. For example, an attacker might simultaneously try to suppress some voters, attract new voters into the election, and introduce a spoiler candidate. Our model provides a unified framework for such varied attacks, and by constructing polynomial-time multiprong attack algorithms we prove that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time.


Practically Stabilizing Atomic Memory

Abstract: A self-stabilizing simulation of a single-writer multi-reader atomic register is presented. The simulation works in asynchronous message-passing systems, and allows processes to crash, as long as at least a majority of them remain working. A key element in the simulation is a new combinatorial construction of a bounded labeling scheme that can accommodate arbitrary labels, i.e., including those not generated by the scheme itself.


The complexity of solving reachability games using value and strategy iteration

Abstract: Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations needed by both of these algorithms for providing non-trivial approximations to the value of a game with N non-terminal positions and m actions for each player in each position. In particular, both algorithms have doubly-exponential complexity. Even when the game given as input has only one non-terminal position, we prove an exponential lower bound on the worst case number of iterations needed to provide non-trivial approximations.


Communication Complexity

Abstract: The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the well-known lower bound methods and prove the exact complexity of certain functions. In the first part of the third section I introduce the random complexity and prove the basic lemmas about it. In the second part I prove a better lower bound for the complexity of all random functions. In the third part I introduce and compare several upper bounds for the complexity of the identity function. In the fourth section I examine the well-known Direct-sum conjecture. I introduce a different model of computation then prove that it is the same as the original one up to a constant factor. This new model is used to bound the Amortized Time Complexity of a function by the number of the leaves of its protocol-tree. After this I examine the Direct-sum problem in case of Partial Information and in the Random case. In the last section I introduce the well-known hierarchy classes, the reducibility and the completeness of series of functions. Then I define the class PSPACE and Oracles in the communication complexity model and prove some basic claims about them.


NP=PSPACE

Abstract: This paper has been withdrawn by the author due to a misunderstanding about 3QBF.


Maximum Bipartite Matching Size And Application to Cuckoo Hashing

Abstract: Cuckoo hashing with a stash is a robust multiple choice hashing scheme with high memory utilization that can be used in many network device applications. Unfortunately, for memory loads beyond 0.5, little is known on its performance. In this paper, we analyze its average performance over such loads. We tackle this problem by recasting the problem as an analysis of the expected maximum matching size of a given random bipartite graph. We provide exact results for any finite system, and also deduce asymptotic results as the memory size increases. We further consider other variants of this problem, and finally evaluate the performance of our models on Internet backbone traces. More generally, our results give a tight lower bound on the size of the stash needed for any multiple-choice hashing scheme.


On Flat Polyhedra deriving from Alexandrov's Theorem

Abstract: We show that there is a straightforward algorithm to determine if the polyhedron guaranteed to exist by Alexandrov's gluing theorem is a degenerate flat polyhedron, and to reconstruct it from the gluing instructions. The algorithm runs in O(n^3) time for polygons whose gluings are specified by n labels.


Parameterizing by the Number of Numbers

Abstract: The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for ILPF to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system description. We consider several core problems of this kind relevant to number-of-numbers parameterization. Our main hardness result considers the problem: given a non-deterministic Mealy machine M (a finite state automaton outputting a letter on each transition), an input word x, and a census requirement c for the output word specifying how many times each letter of the output alphabet should be written, decide whether there exists a computation of M reading x that outputs a word y that meets the requirement c. We show that this problem is hard for W[1]. If the question is whether there exists an input word x such that a computation of M on x outputs a word that meets c, the problem becomes fixed-parameter tractable.


Reinforcement Learning via AIXI Approximation

Abstract: This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.


A Tight Bound on the Maximum Interference of Random Sensors in the Highway Model

Abstract: Consider $n$ sensors whose positions are represented by $n$ uniform, independent and identically distributed random variables assuming values in the open unit interval $(0,1)$. A natural way to guarantee connectivity in the resulting sensor network is to assign to each sensor as its range, the maximum of the two possible distances to its two neighbors. The interference at a given sensor is defined as the number of sensors that have this sensor within their range. In this paper we prove that the expected maximum interference of the sensors is $\Theta (\sqrt{\ln n})$.


Comparative Studies of Programming Languages; Course Lecture Notes

Abstract: Lecture notes for the Comparative Studies of Programming Languages course, COMP6411, taught at the Department of Computer Science and Software Engineering, Faculty of Engineering and Computer Science, Concordia University, Montreal, QC, Canada. These notes include a compiled book of primarily related articles from the Wikipedia, the Free Encyclopedia, as well as Comparative Programming Languages book and other resources, including our own. The original notes were compiled by Dr. Paquet.


Equivalence Checking in Embedded Systems Design Verification

Abstract: In this report we focus on some aspects related to modeling and formal verification of embedded systems. Many models have been proposed to represent embedded systems. These models encompass a broad range of styles, characteristics, and application domains and include the extensions of finite state machines, data flow graphs, communication processes and Petri nets. In this report, we have used a PRES+ model (Petri net based Representation for Embedded Systems) as an extension of classical Petri net model that captures concurrency, timing behaviour of embedded systems; it allows systems to be representative in different levels of abstraction and improves expressiveness by allowing the token to carry information. Modeling using PRES+, as discussed above, may be convenient for specifying the input behaviour because it supports concurrency. However, there is no equivalence checking method reported in the literature for PRES+ models to the best of our knowledge. In contrast, equivalence checking of FSMD models exist. As a first step, therefore, we seek to devise an algorithm to translate PRES+ models to FSMD models.


Symmetric Submodular Function Minimization Under Hereditary Family Constraints

Abstract: We present an efficient algorithm to find non-empty minimizers of a symmetric submodular function over any family of sets closed under inclusion. This for example includes families defined by a cardinality constraint, a knapsack constraint, a matroid independence constraint, or any combination of such constraints. Our algorithm make $O(n^3)$ oracle calls to the submodular function where $n$ is the cardinality of the ground set. In contrast, the problem of minimizing a general submodular function under a cardinality constraint is known to be inapproximable within $o(\sqrt{n/\log n})$ (Svitkina and Fleischer [2008]). The algorithm is similar to an algorithm of Nagamochi and Ibaraki [1998] to find all nontrivial inclusionwise minimal minimizers of a symmetric submodular function over a set of cardinality $n$ using $O(n^3)$ oracle calls. Their procedure in turn is based on Queyranne's algorithm [1998] to minimize a symmetric submodular


Matroid Secretary Problem in the Random Assignment Model

Abstract: In the Matroid Secretary Problem, introduced by Babaioff et al. [SODA 2007], the elements of a given matroid are presented to an online algorithm in random order. When an element is revealed, the algorithm learns its weight and decides whether or not to select it under the restriction that the selected elements form an independent set in the matroid. The objective is to maximize the total weight of the chosen elements. In the most studied version of this problem, the algorithm has no information about the weights beforehand. We refer to this as the zero information model. In this paper we study a different model, also proposed by Babaioff et al., in which the relative order of the weights is random in the matroid. To be precise, in the random assignment model, an adversary selects a collection of weights that are randomly assigned to the elements of the matroid. Later, the elements are revealed to the algorithm in a random order independent of the assignment. Our main result is the first constant competitive algorithm for the matroid secretary problem in the random assignment model. This solves an open question of Babaioff et al. Our algorithm achieves a competitive ratio of $2e^2/(e-1)$. It exploits the notion of principal partition of a matroid, its decomposition into uniformly dense minors, and a $2e$-competitive algorithm for uniformly dense matroids we also develop. As additional results, we present simple constant competitive algorithms in the zero information model for various classes of matroids including cographic, low density and the case when every element is in a small cocircuit. In the same model, we also give a $ke$-competitive algorithm for $k$-column sparse linear matroids, and a new $O(\log r)$-competitive algorithm for general matroids of rank $r$ which only uses the relative order of the weights seen and not their numerical value, as previously needed.


What's wrong with Phong - Designers' appraisal of shading in CAD-systems

Abstract: The Phong illumination model is still widely used in realtime 3D visualization systems. The aim of this article is to document problems with the Phong illumination model that are encountered by an important professional user group, namely digital designers. This leads to a visual evaluation of Phong illumination, which at least in this condensed form seems still to be missing in the literature. It is hoped that by explicating these flaws, awareness about the limitations and interdependencies of the model will increase, both among fellow users, and among researchers and developers.


Optimal Path Planning under Temporal Logic Constraints

Abstract: In this paper we present a method for automatically generating optimal robot trajectories satisfying high level mission specifications. The motion of the robot in the environment is modeled as a general transition system, enhanced with weighted transitions. The mission is specified by a general linear temporal logic formula. In addition, we require that an optimizing proposition must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot trajectory which minimizes the cost function. The problem is motivated by applications in robotic monitoring and data gathering. In this setting, the optimizing proposition is satisfied at all locations where data can be uploaded, and the entire formula specifies a complex (and infinite horizon) data collection mission. Our method utilizes B\"uchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal logic specification. We then present a graph algorithm which computes a path corresponding to the optimal robot trajectory. We also present an implementation for a robot performing a data gathering mission in a road network.


Faster Replacement Paths

Abstract: The replacement paths problem for directed graphs is to find for given nodes s and t and every edge e on the shortest path between them, the shortest path between s and t which avoids e. For unweighted directed graphs on n vertices, the best known algorithm runtime was \tilde{O}(n^{2.5}) by Roditty and Zwick. For graphs with integer weights in {-M,...,M}, Weimann and Yuster recently showed that one can use fast matrix multiplication and solve the problem in O(Mn^{2.584}) time, a runtime which would be O(Mn^{2.33}) if the exponent \omega of matrix multiplication is 2. We improve both of these algorithms. Our new algorithm also relies on fast matrix multiplication and runs in O(M n^{\omega} polylog(n)) time if \omega>2 and O(n^{2+\eps}) for any \eps>0 if \omega=2. Our result shows that, at least for small integer weights, the replacement paths problem in directed graphs may be easier than the related all pairs shortest paths problem in directed graphs, as the current best runtime for the latter is \Omega(n^{2.5}) time even if \omega=2.


Darknet-Based Inference of Internet Worm Temporal Characteristics

Abstract: Internet worm attacks pose a significant threat to network security and management. In this work, we coin the term Internet worm tomography as inferring the characteristics of Internet worms from the observations of Darknet or network telescopes that monitor a routable but unused IP address space. Under the framework of Internet worm tomography, we attempt to infer Internet worm temporal behaviors, i.e., the host infection time and the worm infection sequence, and thus pinpoint patient zero or initially infected hosts. Specifically, we introduce statistical estimation techniques and propose method of moments, maximum likelihood, and linear regression estimators. We show analytically and empirically that our proposed estimators can better infer worm temporal characteristics than a naive estimator that has been used in the previous work. We also demonstrate that our estimators can be applied to worms using different scanning strategies such as random scanning and localized scanning.


Phase Changes in the Evolution of the IPv4 and IPv6 AS-Level Internet Topologies

Abstract: In this paper we investigate the evolution of the IPv4 and IPv6 Internet topologies at the autonomous system (AS) level over a long period of time.We provide abundant empirical evidence that there is a phase transition in the growth trend of the two networks. For the IPv4 network, the phase change occurred in 2001. Before then the network's size grew exponentially, and thereafter it followed a linear growth. Changes are also observed around the same time for the maximum node degree, the average node degree and the average shortest path length. For the IPv6 network, the phase change occurred in late 2006. It is notable that the observed phase transitions in the two networks are different, for example the size of IPv6 network initially grew linearly and then shifted to an exponential growth. Our results show that following decades of rapid expansion up to the beginning of this century, the IPv4 network has now evolved into a mature, steady stage characterised by a relatively slow growth with a stable network structure; whereas the IPv6 network, after a slow startup process, has just taken off to a full speed growth. We also provide insight into the possible impact of IPv6-over-IPv4 tunneling deployment scheme on the evolution of the IPv6 network. The Internet topology generators so far are based on an inexplicit assumption that the evolution of Internet follows non-changing dynamic mechanisms. This assumption, however, is invalidated by our results.Our work reveals insights into the Internet evolution and provides inputs to future AS-Level Internet models.


Acyclic Edge Coloring of Triangle Free Planar Graphs

Abstract: An $acyclic$ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The \emph{acyclic chromatic index} of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by $a'(G)$. It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that $a'(G)\le \Delta+2$, where $\Delta =\Delta(G)$ denotes the maximum degree of the graph. If every induced subgraph $H$ of $G$ satisfies the condition $\vert E(H) \vert \le 2\vert V(H) \vert -1$, we say that the graph $G$ satisfies $Property\ A$. In this paper, we prove that if $G$ satisfies $Property\ A$, then $a'(G)\le \Delta + 3$. Triangle free planar graphs satisfy $Property\ A$. We infer that $a'(G)\le \Delta + 3$, if $G$ is a triangle free planar graph. Another class of graph which satisfies $Property\ A$ is 2-fold graphs (union of two forests).


Is Content Publishing in BitTorrent Altruistic or Profit-Driven

Abstract: BitTorrent is the most popular P2P content delivery application where individual users share various type of content with tens of thousands of other users. The growing popularity of BitTorrent is primarily due to the availability of valuable content without any cost for the consumers. However, apart from required resources, publishing (sharing) valuable (and often copyrighted) content has serious legal implications for user who publish the material (or publishers). This raises a question that whether (at least major) content publishers behave in an altruistic fashion or have other incentives such as financial. In this study, we identify the content publishers of more than 55k torrents in 2 major BitTorrent portals and examine their behavior. We demonstrate that a small fraction of publishers are responsible for 66% of published content and 75% of the downloads. Our investigations reveal that these major publishers respond to two different profiles. On one hand, antipiracy agencies and malicious publishers publish a large amount of fake files to protect copyrighted content and spread malware respectively. On the other hand, content publishing in BitTorrent is largely driven by companies with financial incentive. Therefore, if these companies lose their interest or are unable to publish content, BitTorrent traffic/portals may disappear or at least their associated traffic will significantly reduce.


A measure of state transition of collective of stateless automata in discrete environment

Abstract: In this work a collective of interacting stateless automata in a discrete geometric environment is considered as an integral automata-like computational dynamic object. For such distributed on the environment object different approaches to definition of the measure of state transition are possible. We propose a geometric approach for defining what a state is.


A Note on Semantic Web Services Specification and Composition in Constructive Description Logics

Abstract: The idea of the Semantic Web is to annotate Web content and services with computer interpretable descriptions with the aim to automatize many tasks currently performed by human users. In the context of Web services, one of the most interesting tasks is their composition. In this paper we formalize this problem in the framework of a constructive description logic. In particular we propose a declarative service specification language and a calculus for service composition. We show by means of an example how this calculus can be used to define composed Web services and we discuss the problem of automatic service synthesis.


Heapable Sequences and Subsequences

Abstract: Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number. In this paper we consider a variety of problems related to heapable sequences and subsequences that do not appear to have been studied previously. Our motivation for introducing these concepts is two-fold. First, such problems correspond to natural extensions of the well-known secretary problem for hiring an organization with a hierarchical structure. Second, from a purely combinatorial perspective, our problems are interesting variations on similar longest increasing subsequence problems, a problem paradigm that has led to many deep mathematical connections. We provide several basic results. We obtain an efficient algorithm for determining the heapability of a sequence, and also prove that the question of whether a sequence can be arranged in a complete binary heap is NP-hard. Regarding subsequences we show that, with high probability, the longest heapable subsequence of a random permutation of n numbers has length (1 - o(1)) n, and a subsequence of length (1 - o(1)) n can in fact be found online with high probability. We similarly show that for a random permutation a subsequence that yields a complete heap of size \alpha n for a constant \alpha can be found with high probability. Our work highlights the interesting structure underlying this class of subsequence problems, and we leave many further interesting variations open for future work.


A methodological approach on the architectural development of integrated e-learning systems

Abstract: This study presents a methodological approach to the development of integrated e-learning systems that is used in the creation of educational content for standard Learning Management Systems.


Neural Network Based Reconstruction of a 3D Object from a 2D Wireframe

Abstract: We propose a new approach for constructing a 3D representation from a 2D wireframe drawing. A drawing is simply a parallel projection of a 3D object onto a 2D surface; humans are able to recreate mental 3D models from 2D representations very easily, yet the process is very difficult to emulate computationally. We hypothesize that our ability to perform this construction relies on the angles in the 2D scene, among other geometric properties. Being able to reproduce this reconstruction process automatically would allow for efficient and robust 3D sketch interfaces. Our research focuses on the relationship between 2D geometry observable in the sketch and 3D geometry derived from a potential 3D construction. We present a fully automated system that constructs 3D representations from 2D wireframes using a neural network in conjunction with a genetic search algorithm.


A Brief Introduction to Temporality and Causality

Abstract: Causality is a non-obvious concept that is often considered to be related to temporality. In this paper we present a number of past and present approaches to the definition of temporality and causality from philosophical, physical, and computational points of view. We note that time is an important ingredient in many relationships and phenomena. The topic is then divided into the two main areas of temporal discovery, which is concerned with finding relations that are stretched over time, and causal discovery, where a claim is made as to the causal influence of certain events on others. We present a number of computational tools used for attempting to automatically discover temporal and causal relations in data.


Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry

Abstract: We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with symmetry groups p3m1, p4m, or p6m that have polyominoes or polyiamonds as fundamental domains. We display the algorithms' output and give enumeration tables for small values of n. This expands on our earlier works (Fukuda et al 2006, 2008).


Ranking with Submodular Valuations

Abstract: We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set $[m]$, and a collection of $n$ monotone submodular set functions $f^1, \ldots, f^n$, where each $f^i: 2^{[m]} \to R_+$. An additional ingredient of the input is a weight vector $w \in R_+^n$. The objective is to find a linear ordering of the ground set elements that minimizes the weighted cover time of the functions. The cover time of a function is the minimal number of elements in the prefix of the linear ordering that form a set whose corresponding function value is greater than a unit threshold value. Our main contribution is an $O(\ln(1 / \epsilon))$-approximation algorithm for the problem, where $\epsilon$ is the smallest non-zero marginal value that any function may gain from some element. Our algorithm orders the elements using an adaptive residual updates scheme, which may be of independent interest. We also prove that the problem is $\Omega(\ln(1 / \epsilon))$-hard to approximate, unless P = NP. This implies that the outcome of our algorithm is optimal up to constant factors.


A general method for deciding about logically constrained issues

Abstract: A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed. The method has two variants, dual of each other, whose revised degrees of belief are respectively above and below the original ones. The upper [resp. lower] revised degrees of belief are uniquely characterized as the lowest [resp. highest] ones that are invariant by a certain max-min [resp. min-max] operation determined by the logical constraints. In both variants, making balance between the revised degree of belief of a proposition and that of its negation leads to decisions that are ensured to be consistent with the logical constraints. These decisions are ensured to agree with the majority criterion as applied to the original degrees of belief whenever this gives a consistent result. They are also also ensured to satisfy a property of respect for unanimity about any particular issue, as well as a property of monotonicity with respect to the original degrees of belief. The application of the method to certain special domains comes down to well established or increasingly accepted methods, such as the single-link method of cluster analysis and the method of paths in preferential voting.


Sublinear Time Motif Discovery from Multiple Sequences

Abstract: A natural probabilistic model for motif discovery has been used to experimentally test the quality of motif discovery programs. In this model, there are $k$ background sequences, and each character in a background sequence is a random character from an alphabet $\Sigma$. A motif $G=g_1g_2...g_m$ is a string of $m$ characters. Each background sequence is implanted a probabilistically generated approximate copy of $G$. For a probabilistically generated approximate copy $b_1b_2...b_m$ of $G$, every character $b_i$ is probabilistically generated such that the probability for $b_i\neq g_i$ is at most $\alpha$. We develop three algorithms that under the probabilistic model can find the implanted motif with high probability via a tradeoff between computational time and the probability of mutation. The methods developed in this paper have been used in the software implementation. We observed some encouraging results that show improved performance for motif detection compared with other softwares.


XML Reconstruction View Selection in XML Databases: Complexity Analysis and Approximation Scheme

Abstract: Query evaluation in an XML database requires reconstructing XML subtrees rooted at nodes found by an XML query. Since XML subtree reconstruction can be expensive, one approach to improve query response time is to use reconstruction views - materialized XML subtrees of an XML document, whose nodes are frequently accessed by XML queries. For this approach to be efficient, the principal requirement is a framework for view selection. In this work, we are the first to formalize and study the problem of XML reconstruction view selection. The input is a tree $T$, in which every node $i$ has a size $c_i$ and profit $p_i$, and the size limitation $C$. The target is to find a subset of subtrees rooted at nodes $i_1,\cdots, i_k$ respectively such that $c_{i_1}+\cdots +c_{i_k}\le C$, and $p_{i_1}+\cdots +p_{i_k}$ is maximal. Furthermore, there is no overlap between any two subtrees selected in the solution. We prove that this problem is NP-hard and present a fully polynomial-time approximation scheme (FPTAS) as a solution.


The Complexity of Testing Monomials in Multivariate Polynomials

Abstract: The work in this paper is to initiate a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its sum-product expansion. The complexity aspects of this problem and its variants are investigated with two folds of objectives. One is to understand how this problem relates to critical problems in complexity, and if so to what extent. The other is to exploit possibilities of applying algebraic properties of polynomials to the study of those problems. A series of results about $\Pi\Sigma\Pi$ and $\Pi\Sigma$ polynomials are obtained in this paper, laying a basis for further study along this line.


Algorithms for Testing Monomials in Multivariate Polynomials

Abstract: This paper is our second step towards developing a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by an arithmetic circuit has some types of monomials in its sum-product expansion. The complexity aspects of this problem and its variants have been investigated in our first paper by Chen and Fu (2010), laying a foundation for further study. In this paper, we present two pairs of algorithms. First, we prove that there is a randomized $O^*(p^k)$ time algorithm for testing $p$-monomials in an $n$-variate polynomial of degree $k$ represented by an arithmetic circuit, while a deterministic $O^*(6.4^k + p^k)$ time algorithm is devised when the circuit is a formula, here $p$ is a given prime number. Second, we present a deterministic $O^*(2^k)$ time algorithm for testing multilinear monomials in $\Pi_m\Sigma_2\Pi_t\times \Pi_k\Pi_3$ polynomials, while a randomized $O^*(1.5^k)$ algorithm is given for these polynomials. The first algorithm extends the recent work by Koutis (2008) and Williams (2009) on testing multilinear monomials. Group algebra is exploited in the algorithm designs, in corporation with the randomized polynomial identity testing over a finite field by Agrawal and Biswas (2003), the deterministic noncommunicative polynomial identity testing by Raz and Shpilka (2005) and the perfect hashing functions by Chen {\em at el.} (2007). Finally, we prove that testing some special types of multilinear monomial is W[1]-hard, giving evidence that testing for specific monomials is not fixed-parameter tractable.