OpenRaiser/Intern-Atlas huggingface dataset:
Comments on Cut-Set Bounds on Network Function Computation
Venue: arXiv cs.IT 2017
Year: 2017

A function computation problem in directed acyclic networks has been considered in the literature, where a sink node wants to compute a target function with the inputs generated at multiple source nodes. The network links are error-free but capacity-limited, and the intermediate network nodes perform network coding. The target function is required to be computed with zero error. The computing rate of a network code is measured by the average number of times that the target function can be computed for one use of the network, i.e., each link in the network is used at most once. In the papers [1], [2], two cut-set bounds were proposed on the computing rate. However, we show in this paper that these bounds are not valid for general network function computation problems. We analyze the arguments that lead to the invalidity of these bounds and fix the issue with a new cut-set bound, where a new equivalence relation associated with the inputs of the target function is used. Our bound is qualified for general target functions and network topologies. We also show that our bound is tight for some special cases where the computing capacity is known. Moreover, some results in [11], [12] were proved using the invalid upper bound in [1] and hence their correctness needs further justification. We also justify their validity in the paper.
The Logic of Counting Query Answers
Venue: arXiv cs.LO 2017
Year: 2017

We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently expressed, in senses that are made precise and that are motivated by the wish to understand tractable cases of the counting problem.
Unifying Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes
Venue: arXiv cs.LO 2017
Year: 2017

We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
Reversible Causal Graph Dynamics
Venue: arXiv cs.DM 2017
Year: 2017

Causal Graph Dynamics extend Cellular Automata to arbitrary, bounded-degree, time-varying graphs. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of physics-like symmetries: shift-invariance (it acts everywhere the same) and causality (information has a bounded speed of propagation). We add a further physics-like symmetry, namely reversibility. KEYWORDS: Bijective, invertible, injective, surjective, one-to-one, onto, Cayley graphs, Hedlund, Block representation, Lattice-gas automaton, Reversible Cellular Automata.
Deterministic and Probabilistic Binary Search in Graphs
Venue: arXiv cs.DS 2017
Year: 2017

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - δ)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/δ))$ queries, and identifies the target correctly with probability at leas $1-δ$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $Σ_{2k-1}$ in the polynomial hierarchy, and hardness for $Σ_{2k-5}$.
Estimating the Probability of Meeting a Deadline in Hierarchical Plans
Venue: arXiv cs.AI 2017
Year: 2017

Given a hierarchical plan (or schedule) with uncertain task times, we propose a deterministic polynomial (time and memory) algorithm for estimating the probability that its meets a deadline, or, alternately, that its {\em makespan} is less than a given duration. Approximation is needed as it is known that this problem is NP-hard even for sequential plans (just, a sum of random variables). In addition, we show two new complexity results: (1) Counting the number of events that do not cross deadline is \#P-hard; (2)~Computing the expected makespan of a hierarchical plan is NP-hard. For the proposed approximation algorithm, we establish formal approximation bounds and show that the time and memory complexities grow polynomially with the required accuracy, the number of nodes in the plan, and with the size of the support of the random variables that represent the durations of the primitive tasks. We examine these approximation bounds empirically and demonstrate, using task networks taken from the literature, how our scheme outperforms sampling techniques and exact computation in terms of accuracy and run-time. As the empirical data shows much better error bounds than guaranteed, we also suggest a method for tightening the bounds in some cases.
The Role of Data Cap in Optimal Two-part Network Pricing
Venue: arXiv cs.NI 2017
Year: 2017

Internet services are traditionally priced at flat rates; however, many Internet service providers (ISPs) have recently shifted towards two-part tariffs where a data cap is imposed to restrain data demand from heavy users. Although the two-part tariff could generally increase the revenue for ISPs and has been supported by the US FCC, the role of data cap and its optimal pricing structures are not well understood. In this article, we study the impact of data cap on the optimal two-part pricing schemes for congestion-prone service markets. We model users' demand and preferences over pricing and congestion alternatives and derive the market share and congestion of service providers under a market equilibrium. Based on the equilibrium model, we characterize the two-part structures of the revenue- and welfare-optimal pricing schemes. Our results reveal that 1) the data cap provides a mechanism for ISPs to transition from the flat-rate to pay-as-you-go type of schemes, 2) both the revenue and welfare objectives of the ISP will drive the optimal pricing towards usage-based schemes with diminishing data caps, and 3) the welfare-optimal tariff comprises lower fees than the revenue-optimal counterpart, suggesting that regulators might want to promote usage-based pricing but regulate the lump-sum and per-unit fees.
Models and Information Rates for Multiuser Optical Fiber Channels with Nonlinearity and Dispersion
Venue: arXiv cs.IT 2017
Year: 2017

Two discrete-time interference channel models are developed for information transmission over a single span of optical fiber using wavelength-division multiplexing (WDM) and lumped amplification. The models are derived from the nonlinear Schroedinger (NLS) equation by including the nonlinear phenomena of self-phase modulation (SPM) and cross-phase modulation (XPM) but ignoring four-wave mixing (FWM), polarization effects and group velocity dispersion (GVD) within WDM bands. The first model also ignores GVD across WDM bands, referred to as group velocity mistmatch (GVM). For the case of two users, a new technique called "interference focusing" is proposed where each carrier achieves the capacity pre-log 1, thereby doubling the pre-log of 1/2 achieved by using conventional methods. For three users, interference focusing is also useful under certain conditions. The second model captures GVM and the effect of filtering at the receivers in addition to SPM and XPM. In a 3-user system, it is shown that all users can achieve the maximum pre-log factor 1 simultaneously by using interference focusing, a time-limited pulse and a bank of filters at the receivers.
Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design
Venue: arXiv cs.SY 2017
Year: 2017

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control system. The conditions have a simple geometrical interpretation, can be written as a convex feasibility problem, and are invariant under coordinate changes. We show that these conditions are necessary and sufficient for feedback linearizable systems, and also derive novel convex criteria for exponential stabilization of a nonlinear submanifold of state space. We illustrate the benefits of convexity by constructing a controller for an unstable polynomial system that combines local optimality and global stability, using a metric found via sum-of-squares programming.
Is language evolution grinding to a halt? The scaling of lexical turbulence in English fiction suggests it is not
Venue: arXiv cs.CL 2017
Year: 2017

Of basic interest is the quantification of the long term growth of a language's lexicon as it develops to more completely cover both a culture's communication requirements and knowledge space. Here, we explore the usage dynamics of words in the English language as reflected by the Google Books 2012 English Fiction corpus. We critique an earlier method that found decreasing birth and increasing death rates of words over the second half of the 20th Century, showing death rates to be strongly affected by the imposed time cutoff of the arbitrary present and not increasing dramatically. We provide a robust, principled approach to examining lexical evolution by tracking the volume of word flux across various relative frequency thresholds. We show that while the overall statistical structure of the English language remains stable over time in terms of its raw Zipf distribution, we find evidence of an enduring `lexical turbulence': The flux of words across frequency thresholds from decade to decade scales superlinearly with word rank and exhibits a scaling break we connect to that of Zipf's law. To better understand the changing lexicon, we examine the contributions to the Jensen-Shannon divergence of individual words crossing frequency thresholds. We also find indications that scholarly works about fiction are strongly represented in the 2012 English Fiction corpus, and suggest that a future revision of the corpus should attempt to separate critical works from fiction itself.
The Complexity of Phylogeny Constraint Satisfaction Problems
Venue: arXiv cs.CC 2017
Year: 2017

We systematically study the computational complexity of a broad class of computational problems in phylogenetic reconstruction. The class contains for example the rooted triple consistency problem, forbidden subtree problems, the quartet consistency problem, and many other problems studied in the bioinformatics literature. The studied problems can be described as \emph{constraint satisfaction problems} where the constraints have a first-order definition over the rooted triple relation. We show that every such phylogeny problem can be solved in polynomial time or is NP-complete. On the algorithmic side, we generalize a well-known polynomial-time algorithm of Aho, Sagiv, Szymanski, and Ullman for the rooted triple consistency problem. Our algorithm repeatedly solves linear equation systems to construct a solution in polynomial time. We then show that every phylogeny problem that cannot be solved by our algorithm is NP-complete. Our classification establishes a dichotomy for a large class of infinite structures that we believe is of independent interest in universal algebra, model theory, and topology. The proof of our main result combines results and techniques from various research areas: a recent classification of the model-complete cores of the reducts of the homogeneous binary branching C-relation, Leeb's Ramsey theorem for rooted trees, and universal algebra.
Projective simulation with generalization
Venue: arXiv cs.AI 2017
Year: 2017

The ability to generalize is an important feature of any intelligent agent. Not only because it may allow the agent to cope with large amounts of data, but also because in some environments, an agent with no generalization capabilities cannot learn. In this work we outline several criteria for generalization, and present a dynamic and autonomous machinery that enables projective simulation agents to meaningfully generalize. Projective simulation, a novel, physical approach to artificial intelligence, was recently shown to perform well in standard reinforcement learning problems, with applications in advanced robotics as well as quantum experiments. Both the basic projective simulation model and the presented generalization machinery are based on very simple principles. This allows us to provide a full analytical analysis of the agent's performance and to illustrate the benefit the agent gains by generalizing. Specifically, we show that already in basic (but extreme) environments, learning without generalization may be impossible, and demonstrate how the presented generalization machinery enables the projective simulation agent to learn.
A closed equation in time domain for band-limited extensions of one-sided sequences
Venue: arXiv cs.IT 2017
Year: 2017

The paper suggests a method of optimal extension of one-sided semi-infinite sequences of a general type by traces of band-limited sequences in deterministic setting, i.e. without probabilistic assumptions. The method requires to solve a closed linear equation in the time domain connecting the past observations of the underlying process with the future values of the band-limited process. Robustness of the solution with respect to the input errors and data truncation is established in the framework of Tikhonov regularization.
Engineering Methods for Differentially Private Histograms: Efficiency Beyond Utility
Venue: arXiv cs.DB 2017
Year: 2017

Publishing histograms with $ε$-differential privacy has been studied extensively in the literature. Existing schemes aim at maximizing the utility of the published data, while previous experimental evaluations analyze the privacy/utility trade-off. In this paper we provide the first experimental evaluation of differentially private methods that goes beyond utility, emphasizing also on another important aspect, namely efficiency. Towards this end, we first observe that all existing schemes are comprised of a small set of common blocks. We then optimize and choose the best implementation for each block, determine the combinations of blocks that capture the entire literature, and propose novel block combinations. We qualitatively assess the quality of the schemes based on the skyline of efficiency and utility, i.e., based on whether a method is dominated on both aspects or not. Using exhaustive experiments on four real datasets with different characteristics, we conclude that there are always trade-offs in terms of utility and efficiency. We demonstrate that the schemes derived from our novel block combinations provide the best trade-offs for time critical applications. Our work can serve as a guide to help practitioners engineer a differentially private histogram scheme depending on their application requirements.
On minimal free resolutions of sub-permanents and other ideals arising in complexity theory
Venue: arXiv cs.CC 2017
Year: 2017

We compute the linear strand of the minimal free resolution of the ideal generated by k x k sub-permanents of an n x n generic matrix and of the ideal generated by square-free monomials of degree k. The latter calculation gives the full minimal free resolution by work of Biagioli-Faridi-Rosas. Our motivation is to lay groundwork for the use of commutative algebra in algebraic complexity theory. We also compute several Hilbert functions relevant for complexity theory.
Satisfiability of Modal Inclusion Logic: Lax and Strict Semantics
Venue: arXiv cs.LO 2017
Year: 2017

We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be EXPTIME-complete on general structures. Finally, we show how for a specific class of structures NEXPTIME-completeness for these problems under strict semantics can be achieved.
A Practical and Worst-Case Efficient Algorithm for Divisor Methods of Apportionment
Venue: arXiv cs.DS 2017
Year: 2017

Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms that implement divisor methods: one by Cheng and Eppstein (ISAAC, 2014) has worst-case optimal running time but is complex, while the other (Pukelsheim, 2014) is relatively simple and fast in practice but does not offer worst-case guarantees. We demonstrate that the former algorithm is much slower than the other in practice and propose a novel algorithm that avoids the shortcomings of both. We investigate the running-time behavior of the three contenders in order to determine which is most useful in practice.
Edit Distance for Pushdown Automata
Venue: arXiv cs.FL 2017
Year: 2017

The edit distance between two words $w_1, w_2$ is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform $w_1$ to $w_2$. The edit distance generalizes to languages $\mathcal{L}_1, \mathcal{L}_2$, where the edit distance from $\mathcal{L}_1$ to $\mathcal{L}_2$ is the minimal number $k$ such that for every word from $\mathcal{L}_1$ there exists a word in $\mathcal{L}_2$ with edit distance at most $k$. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for the following problems: (1)~deciding whether, for a given threshold $k$, the edit distance from a pushdown automaton to a finite automaton is at most $k$, and (2)~deciding whether the edit distance from a pushdown automaton to a finite automaton is finite.
On a spatial-temporal decomposition of the optical flow
Venue: arXiv cs.CV 2017
Year: 2017

In this paper we present a decomposition algorithm for computation of the spatial-temporal optical flow of a dynamic image sequence. We consider several applications, such as the extraction of temporal motion features and motion detection in dynamic sequences under varying illumination conditions, such as they appear for instance in psychological flickering experiments. For the numerical implementation we are solving an integro-differential equation by a fixed point iteration. For comparison purposes we use a standard time dependent optical flow algorithm, which in contrast to our method, constitutes in solving a spatial-temporal differential equation.
Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems
Venue: arXiv cs.DC 2017
Year: 2017

In this paper, we show that the protocol complex of a Byzantine synchronous system can remain $(k - 1)$-connected for up to $\lceil t/k \rceil$ rounds, where $t$ is the maximum number of Byzantine processes, and $t \ge k \ge 1$. This topological property implies that $\lceil t/k \rceil + 1$ rounds are necessary to solve $k$-set agreement in Byzantine synchronous systems, compared to $\lfloor t/k \rfloor + 1$ rounds in synchronous crash-failure systems. We also show that our connectivity bound is tight as we indicate solutions to Byzantine $k$-set agreement in exactly $\lceil t/k \rceil + 1$ synchronous rounds, at least when $n$ is suitably large compared to $t$. In conclusion, we see how Byzantine failures can potentially require one extra round to solve $k$-set agreement, and, for $n$ suitably large compared to $t$, at most that.
A Fast Network-Decomposition Algorithm and its Applications to Constant-Time Distributed Computation
Venue: arXiv cs.DC 2017
Year: 2017

A partition $(C_1,C_2,...,C_q)$ of $G = (V,E)$ into clusters of strong (respectively, weak) diameter $d$, such that the supergraph obtained by contracting each $C_i$ is $\ell$-colorable is called a strong (resp., weak) $(d, \ell)$-network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Awerbuch et al. showed that strong $(exp\{O(\sqrt{ \log n \log \log n})\}, exp\{O(\sqrt{ \log n \log \log n})\})$-network-decompositions can be computed in distributed deterministic time $exp\{O(\sqrt{ \log n \log \log n})\}$. The result of Awerbuch et al. was improved by Panconesi and Srinivasan in 1992: in the latter result $d = \ell = exp\{O(\sqrt{\log n})\}$, and the running time is $exp\{O(\sqrt{\log n})\}$ as well. Much more recently Barenboim (2012) devised a distributed randomized constant-time algorithm for computing strong network decompositions with $d = O(1)$. However, the parameter $\ell$ in his result is $O(n^{1/2 + ε})$. In this paper we drastically improve the result of Barenboim and devise a distributed randomized constant-time algorithm for computing strong $(O(1), O(n^ε))$-network-decompositions. As a corollary we derive a constant-time randomized $O(n^ε)$-approximation algorithm for the distributed minimum coloring problem, improving the previously best-known $O(n^{1/2 + ε})$ approximation guarantee. We also derive other improved distributed algorithms for a variety of problems. Most notably, for the extremely well-studied distributed minimum dominating set problem currently there is no known deterministic polylogarithmic-time algorithm. We devise a {deterministic} polylogarithmic-time approximation algorithm for this problem, addressing an open problem of Lenzen and Wattenhofer (2010).