OpenRaiser/Intern-Atlas huggingface dataset:
Communication Lower Bounds via Critical Block Sensitivity
Venue: arXiv cs.CC 2016
Year: 2016

We use critical block sensitivity, a new complexity measure introduced by Huynh and Nordström (STOC 2012), to study the communication complexity of search problems. To begin, we give a simple new proof of the following central result of Huynh and Nordström: if $S$ is a search problem with critical block sensitivity $b$, then every randomised two-party protocol solving a certain two-party lift of $S$ requires $Ω(b)$ bits of communication. Besides simplicity, our proof has the advantage of generalising to the multi-party setting. We combine these results with new critical block sensitivity lower bounds for Tseitin and Pebbling search problems to obtain the following applications: (1) Monotone Circuit Depth: We exhibit a monotone $n$-variable function in NP whose monotone circuits require depth $Ω(n/\log n)$; previously, a bound of $Ω(\sqrt{n})$ was known (Raz and Wigderson, JACM 1992). Moreover, we prove a $Θ(\sqrt{n})$ monotone depth bound for a function in monotone P. (2) Proof Complexity: We prove new rank lower bounds as well as obtain the first length--space lower bounds for semi-algebraic proof systems, including Lovász--Schrijver and Lasserre (SOS) systems. In particular, these results extend and simplify the works of Beame et al. (SICOMP 2007) and Huynh and Nordström.
Average case polyhedral complexity of the maximum stable set problem
Venue: arXiv cs.CC 2016
Year: 2016

We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend on the input graph, which should be encoded solely in the objective function. There we prove a $2^{Ω(n/ \log n)}$ lower bound with probability at least $1 - 2^{-2^n}$ for every LP that is exact for a randomly selected set of instances; each graph on at most n vertices being selected independently with probability $p \geq 2^{-\binom{n/4}{2}+n}$. In the non-uniform model, the constraints of the LP may depend on the input graph, but we allow weights on the vertices. The input graph is sampled according to the G(n, p) model. There we obtain upper and lower bounds holding with high probability for various ranges of p. We obtain a super-polynomial lower bound all the way from $p = Ω(\log^{6+\varepsilon} / n)$ to $p = o (1 / \log n)$. Our upper bound is close to this as there is only an essentially quadratic gap in the exponent, which currently also exists in the worst-case model. Finally, we state a conjecture that would close this gap, both in the average-case and worst-case models.
The Parameterized Complexity of Reasoning Problems Beyond NP
Venue: arXiv cs.CC 2016
Year: 2016

Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at the second level of the Polynomial Hierarchy or even higher, and hence polynomial-time transformations to SAT are not possible, unless the hierarchy collapses. Recent research shows that in certain cases one can break through these complexity barriers by fixed-parameter tractable (fpt) reductions which exploit structural aspects of problem instances in terms of problem parameters. In this paper we develop a general theoretical framework that supports the classification of parameterized problems on whether they admit such an fpt-reduction to SAT or not. This framework is based on several new parameterized complexity classes. As a running example, we use the framework to classify the complexity of the consistency problem for disjunctive answer set programming, with respect to various natural parameters. We underpin the robustness of our theory by providing a characterization of the new complexity classes in terms of weighted QBF satisfiability, alternating Turing machines, and first-order model checking. In addition, we provide a compendium of parameterized problems that are complete for the new complexity classes, including problems related to Knowledge Representation and Reasoning, Logic, and Combinatorics.
Complexity results for generating subgraphs
Venue: arXiv cs.DM 2016
Year: 2016

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space, denoted WCW(G). Let B be a complete bipartite induced subgraph of G on vertex sets of bipartition B_X and B_Y. Then B is generating if there exists an independent set S such that S \cup B_X and S \cup B_Y are both maximal independent sets of G. A relating edge is a generating subgraph in the restricted case that B = K_{1,1}. Deciding whether an input graph G is well-covered is co-NP-complete. Therefore finding WCW(G) is co-NP-hard. Deciding whether an edge is relating is co-NP-complete. Therefore, deciding whether a subgraph is generating is co-NP-complete as well. In this article we discuss the connections among these problems, provide proofs for NP-completeness for several restricted cases, and present polynomial characterizations for some other cases.
A Second Look at Counting Triangles in Graph Streams (revised)
Venue: arXiv cs.DS 2016
Year: 2016

In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with $m$ edges and at least $T$ triangles, we show that an extra look over the stream yields a two-pass treaming algorithm that uses $O(\frac{m}{\eps^{2.5}\sqrt{T}}\polylog(m))$ space and outputs a $(1+\eps)$ approximation of the number of triangles in the graph. This improves upon the two-pass streaming tester of Braverman, Ostrovsky and Vilenchik, ICALP 2013, which distinguishes between triangle-free graphs and graphs with at least $T$ triangle using $O(\frac{m}{T^{1/3}})$ space. Also, in terms of dependence on $T$, we show that more passes would not lead to a better space bound. In other words, we prove there is no constant pass streaming algorithm that distinguishes between triangle-free graphs from graphs with at least $T$ triangles using $O(\frac{m}{T^{1/2+ρ}})$ space for any constant $ρ\ge 0$.
Variations on Memetic Algorithms for Graph Coloring Problems
Venue: arXiv cs.AI 2016
Year: 2016

Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm.This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals.Moreover, a new way of managing diversity is brought by HEAD.These two main differences greatly improve the results, both in terms of solution quality and computational time.HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for \textless{}dsjc1000.9\textgreater{}, 81-colorings for \textless{}flat1000\_76\_0\textgreater{} and even 47-colorings for \textless{}dsjc500.5\textgreater{} and 82-colorings for \textless{}dsjc1000.5\textgreater{}.
Technical Report: Sleep-Route - Routing through Sleeping Sensors
Venue: arXiv cs.NI 2016
Year: 2016

In this article, we propose an energy-efficient data gathering scheme for wireless sensor network called Sleep-Route, which splits the sensor nodes into two sets - active and dormant (low-power sleep). Only the active set of sensor nodes participate in data collection. The sensing values of the dormant sensor nodes are predicted with the help of an active sensor node. Virtual Sensing Framework (VSF) provides the mechanism to predict the sensing values by exploiting the data correlation among the sensor nodes. If the number of active sensor nodes can be minimized, a lot of energy can be saved. The active nodes' selection must fulfill the following constraints - (i) the set of active nodes are sufficient to predict the sensing values of the dormant nodes, (ii) each active sensor nodes can report their data to the sink node (directly or through some other active node(s)). The goal is to select a minimal number of active sensor nodes so that energy savings can be maximized. The optimal set of active node selection raise a combinatorial optimization problem, which we refer as Sleep-Route problem. We show that Sleep-Route problem is NP-hard. Then, we formulate an integer linear program (ILP) to solve the problem optimally. To solve the problem in polynomial time, we also propose a heuristic algorithm that performs near optimally.
Equilibria in multi-player multi-outcome infinite sequential games
Venue: arXiv cs.LO 2016
Year: 2016

We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental approaches: one requires strong topological restrictions on the games, but produces very strong existence results. The other merely requires some very basic determinacy properties to still obtain some existence results. Both results are transfer results: starting with the existence of some equilibria for a small class of games, they allow us to conclude the existence of some type of equilibria for a larger class. To make the abstract results more concrete, we investigate as a special case infinite sequential games with real-valued payoff functions. Depending on the class of payoff functions (continuous, upper semi-continuous, Borel) and whether the game is zero-sum, we obtain various existence results for equilibria. Our results hold for games with two or up to countably many players.
Diffusion-Based Adaptive Distributed Detection: Steady-State Performance in the Slow Adaptation Regime
Venue: arXiv cs.IT 2016
Year: 2016

This work examines the close interplay between cooperation and adaptation for distributed detection schemes over fully decentralized networks. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. The results in the paper establish a fundamental scaling law for the steady-state probabilities of miss-detection and false-alarm in the slow adaptation regime, when the agents interact with each other according to distributed strategies that employ small constant step-sizes. The latter are critical to enable continuous adaptation and learning. The work establishes three key results. First, it is shown that the output of the collaborative process at each agent has a steady-state distribution. Second, it is shown that this distribution is asymptotically Gaussian in the slow adaptation regime of small step-sizes. And third, by carrying out a detailed large deviations analysis, closed-form expressions are derived for the decaying rates of the false-alarm and miss-detection probabilities. Interesting insights are gained. In particular, it is verified that as the step-size $μ$ decreases, the error probabilities are driven to zero exponentially fast as functions of $1/μ$, and that the error exponents increase linearly in the number of agents. It is also verified that the scaling laws governing errors of detection and errors of estimation over networks behave very differently, with the former having an exponential decay proportional to $1/μ$, while the latter scales linearly with decay proportional to $μ$. It is shown that the cooperative strategy allows each agent to reach the same detection performance, in terms of detection error exponents, of a centralized stochastic-gradient solution.
Efficient Background Modeling Based on Sparse Representation and Outlier Iterative Removal
Venue: arXiv cs.CV 2016
Year: 2016

Background modeling is a critical component for various vision-based applications. Most traditional methods tend to be inefficient when solving large-scale problems. In this paper, we introduce sparse representation into the task of large scale stable background modeling, and reduce the video size by exploring its 'discriminative' frames. A cyclic iteration process is then proposed to extract the background from the discriminative frame set. The two parts combine to form our Sparse Outlier Iterative Removal (SOIR) algorithm. The algorithm operates in tensor space to obey the natural data structure of videos. Experimental results show that a few discriminative frames determine the performance of the background extraction. Further, SOIR can achieve high accuracy and high speed simultaneously when dealing with real video sequences. Thus, SOIR has an advantage in solving large-scale tasks.
Coding Schemes with Rate-Limited Feedback that Improve over the Nofeedback Capacity for a Large Class of Broadcast Channels
Venue: arXiv cs.IT 2016
Year: 2016

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the nofeedback capacity region for a large class of channels, including the class of \emph{strictly essentially less-noisy BCs} that we introduce in this article. Examples of strictly essentially less-noisy BCs are the binary symmetric BC (BSBC) or the binary erasure BC (BEBC) with unequal cross-over or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feed back quantization messages about their receive signals. In the first scheme, the transmitter simply \emph{relays} the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme the transmitter first \emph{reconstructs and processes} the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme applies also to memoryless BCs without feedback but with strictly-causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information.
On-line approach to off-line coloring problems on graphs with geometric representations
Venue: arXiv cs.DS 2016
Year: 2016

The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction of triangle-free geometric intersection graphs with arbitrarily large chromatic number due to Pawlik et al. We show that on-line graph coloring problems give rise to classes of game graphs with a natural geometric interpretation. We use this concept to estimate the chromatic number of graphs with geometric representations by finding, for appropriate simpler graphs, on-line coloring algorithms using few colors or proving that no such algorithms exist. We derive upper and lower bounds on the maximum chromatic number that rectangle overlap graphs, subtree overlap graphs, and interval filament graphs (all of which generalize interval overlap graphs) can have when their clique number is bounded. The bounds are absolute for interval filament graphs and asymptotic of the form $(\log\log n)^{f(ω)}$ for rectangle and subtree overlap graphs, where $f(ω)$ is a polynomial function of the clique number and $n$ is the number of vertices. In particular, we provide the first construction of geometric intersection graphs with bounded clique number and with chromatic number asymptotically greater than $\log\log n$. We also introduce a concept of $K_k$-free colorings and show that for some geometric representations, $K_3$-free chromatic number can be bounded in terms of clique number although the ordinary ($K_2$-free) chromatic number cannot. Such a result for segment intersection graphs would imply a well-known conjecture that $k$-quasi-planar geometric graphs have linearly many edges.
A measure of compression gain for new symbols in data-compression
Venue: arXiv cs.IT 2016
Year: 2016

Huffman encoding is often improved by using block codes, for example a 3-block would be an alphabet consisting of each possible combination of three characters. We take the approach of starting with a base alphabet and expanding it to include frequently occurring aggregates of symbols. We prove that the change in compressed message length by the introduction of a new aggregate symbol can be expressed as the difference of two entropies, dependent only on the probabilities and length of the introduced symbol. The expression is independent of the probability of all other symbols in the alphabet. This measure of information gain, for a new symbol, can be applied in data compression methods. We also demonstrate that aggregate symbol alphabets, as opposed to mutually exclusive alphabets have the potential to provide good levels of compression, with a simple experiment. Finally, compression gain as defined in this paper may also be useful for feature selection.
Multiple Access Channel with Common Message and Secrecy constraint
Venue: arXiv cs.IT 2016
Year: 2016

In this paper, we study the problem of secret communication over a multiple-access channel with a common message. Here, we assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. We call this setting as Multiple-Access Wiretap Channel with Common message (MAWC-CM). For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a special case called the switch channel. As well, for a Gaussian version of MAWC-CM, we derive inner and outer bounds on the secrecy capacity region. Providing numerical results for the Gaussian case, we illustrate the comparison between the derived achievable rate region and the outer bound for the considered model and the capacity region of compound multiple access channel.
Behavior recognition and analysis in smart environments for context-aware applications
Venue: arXiv cs.LO 2016
Year: 2016

Providing accurate/suitable information on behaviors in sma\-rt environments is a challenging and crucial task in pervasive computing where context-awareness and pro-activity are of fundamental importance. Behavioral identifications enable to abstract higher-level concepts that are interesting to applications. This work proposes the unified logical-based framework to recognize and analyze behavioral specifications understood as a formal logic language that avoids ambiguity typical for natural languages. Automatically discovering behaviors from sensory data streams as formal specifications is of fundamental importance to build seamless human-computer interactions. Thus, the knowledge about environment behaviors expressed in terms of temporal logic formulas constitutes a base for the reactive and precise reasoning processes to support trustworthy, unambiguous and pro-active decisions for applications that are smart and context-aware.
Covert Communication Gains from Adversary's Ignorance of Transmission Time
Venue: arXiv cs.IT 2016
Year: 2016

The recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit $\mathcal{O}(\sqrt{n})$ bits to Bob in $n$ uses of an additive white Gaussian noise (AWGN) channel while keeping ineffective any detector employed by the adversary; conversely, exceeding this limit either results in detection by the adversary with high probability or non-zero decoding error probability at Bob. This SRL is under the assumption that the adversary knows when Alice transmits (if she transmits); however, in many operational scenarios he does not know this. Hence, here we study the impact of the adversary's ignorance of the time of the communication attempt. We employ a slotted AWGN channel model with $T(n)$ slots each containing $n$ symbol periods, where Alice may use a single slot out of $T(n)$. Provided that Alice's slot selection is secret, the adversary needs to monitor all $T(n)$ slots for possible transmission. We show that this allows Alice to reliably transmit $\mathcal{O}(\min\{\sqrt{n\log T(n)},n\})$ bits to Bob (but no more) while keeping the adversary's detector ineffective. To achieve this gain over SRL, Bob does not have to know the time of transmission provided $T(n)<2^{c_{\rm T}n}$, $c_{\rm T}=\mathcal{O}(1)$.
How to Apply Markov Chains for Modeling Sequential Edit Patterns in Collaborative Ontology-Engineering Projects
Venue: arXiv cs.HC 2016
Year: 2016

With the growing popularity of large-scale collaborative ontology-engineering projects, such as the creation of the 11th revision of the International Classification of Diseases, we need new methods and insights to help project- and community-managers to cope with the constantly growing complexity of such projects. In this paper, we present a novel application of Markov chains to model sequential usage patterns that can be found in the change-logs of collaborative ontology-engineering projects. We provide a detailed presentation of the analysis process, describing all the required steps that are necessary to apply and determine the best fitting Markov chain model. Amongst others, the model and results allow us to identify structural properties and regularities as well as predict future actions based on usage sequences. We are specifically interested in determining the appropriate Markov chain orders which postulate on how many previous actions future ones depend on. To demonstrate the practical usefulness of the extracted Markov chains we conduct sequential pattern analyses on a large-scale collaborative ontology-engineering dataset, the International Classification of Diseases in its 11th revision. To further expand on the usefulness of the presented analysis, we show that the collected sequential patterns provide potentially actionable information for user-interface designers, ontology-engineering tool developers and project-managers to monitor, coordinate and dynamically adapt to the natural development processes that occur when collaboratively engineering an ontology. We hope that presented work will spur a new line of ontology-development tools, evaluation-techniques and new insights, further taking the interactive nature of the collaborative ontology-engineering process into consideration.