OpenRaiser/Intern-Atlas huggingface dataset:
Stochastic Online Shortest Path Routing: The Value of Feedback
Venue: arXiv cs.NI 2017
Year: 2017

This paper studies online shortest path routing over multi-hop networks. Link costs or delays are time-varying and modeled by independent and identically distributed random processes, whose parameters are initially unknown. The parameters, and hence the optimal path, can only be estimated by routing packets through the network and observing the realized delays. Our aim is to find a routing policy that minimizes the regret (the cumulative difference of expected delay) between the path chosen by the policy and the unknown optimal path. We formulate the problem as a combinatorial bandit optimization problem and consider several scenarios that differ in where routing decisions are made and in the information available when making the decisions. For each scenario, we derive a tight asymptotic lower bound on the regret that has to be satisfied by any online routing policy. These bounds help us to understand the performance improvements we can expect when (i) taking routing decisions at each hop rather than at the source only, and (ii) observing per-link delays rather than end-to-end path delays. In particular, we show that (i) is of no use while (ii) can have a spectacular impact. Three algorithms, with a trade-off between computational complexity and performance, are proposed. The regret upper bounds of these algorithms improve over those of the existing algorithms, and they significantly outperform state-of-the-art algorithms in numerical experiments.
Compact Part-Based Shape Spaces for Dense Correspondences
Venue: arXiv cs.GR 2017
Year: 2017

We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble optimization method that improves given coarse correspondences to obtain dense correspondences. Following ideas from minimum description length approaches, it maximizes the compactness of the induced shape space to obtain high-quality correspondences. We make a number of improvements that are important for computer graphics applications: Our approach handles meshes of general topology and handles partial matching between input of varying topology. To this end we introduce a novel part-based generative statistical shape model. We develop a novel analysis algorithm that learns such models from training shapes of varying topology. We also provide a novel synthesis method that can generate new instances with varying part layouts and subject to generic variational constraints. In practical experiments, we obtain a substantial improvement in correspondence quality over state-of-the-art methods. As example application, we demonstrate a system that learns shape families as assemblies of deformable parts and permits real-time editing with continuous and discrete variability.
Linear Temporal Logic for Regular Cost Functions
Venue: arXiv cs.LO 2017
Year: 2017

Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is that exact values are not considered, but only estimated. In this paper, we define an extension of Linear Temporal Logic (LTL) over finite words to describe cost functions. We give an explicit translation from this new logic to two dual form of cost automata, and we show that the natural decision problems for this logic are PSPACE-complete, as it is the case in the classical setting. We then algebraically characterize the expressive power of this logic, using a new syntactic congruence for cost functions introduced in this paper.
Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and their subcodes
Venue: arXiv cs.IT 2017
Year: 2017

We give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks consist in the blind reconstruction either of an Error Correcting Pair (ECP), or an Error Correcting Array (ECA) from the single data of an arbitrary generator matrix of a code. An ECP provides a decoding algorithm that corrects up to $\frac{d^*-1-g}{2}$ errors, where $d^*$ denotes the designed distance and $g$ denotes the genus of the corresponding curve, while with an ECA the decoding algorithm corrects up to $\frac{d^*-1}{2}$ errors. Roughly speaking, for a public code of length $n$ over $\mathbb F_q$, these attacks run in $O(n^4\log (n))$ operations in $\mathbb F_q$ for the reconstruction of an ECP and $O(n^5)$ operations for the reconstruction of an ECA. A probabilistic shortcut allows to reduce the complexities respectively to $O(n^{3+\varepsilon} \log (n))$ and $O(n^{4+\varepsilon})$. Compared to the previous known attack due to Faure and Minder, our attack is efficient on codes from curves of arbitrary genus. Furthermore, we investigate how far these methods apply to subcodes of AG codes.
On generalized Tian Ji's horse racing strategy
Venue: arXiv cs.GT 2017
Year: 2017

Tian Ji's horse racing strategy, a famous Chinese legend, constitutes a promising concept to be applied to important issues in today's competitive environment; this strategy is elaborated on and analyzed by examining the general case. The mathematical formulation concerning the calculation of winning, drawing or losing combinations and probabilities is presented to illustrate the interesting insights on how ancient philosophies could promote thinking in business competitiveness, in particular, the wisdom behind sacrificing the part for the benefit of the whole or sacrificing the short-term objectives in order to gain the long-term goal.
Effective dimension in some general metric spaces
Venue: arXiv cs.CC 2017
Year: 2017

We introduce the concept of effective dimension for a wide class of metric spaces that are not required to have a computable measure. Effective dimension was defined by Lutz in (Lutz 2003) for Cantor space and has also been extended to Euclidean space. Lutz effectivization uses the concept of gale and supergale, our extension of Hausdorff dimension to other metric spaces is also based on a supergale characterization of dimension, which in practice avoids an extra quantifier present in the classical definition of dimension that is based on Hausdorff measure and therefore allows effectivization for small time-bounds. We present here the concept of constructive dimension and its characterization in terms of Kolmogorov complexity, for which we extend the concept of Kolmogorov complexity to any metric space defining the Kolmogorov complexity of a point at a certain precision. Further research directions are indicated.
Semantics and Validation of Shapes Schemas for RDF
Venue: arXiv cs.DB 2017
Year: 2017

We present a formal semantics and proof of soundness for shapes schemas, an expressive schema language for RDF graphs that is the foundation of Shape Expressions Language 2.0. It can be used to describe the vocabulary and the structure of an RDF graph, and to constrain the admissible properties and values for nodes in that graph. The language defines a typing mechanism called shapes against which nodes of the graph can be checked. It includes an algebraic grouping operator, a choice operator and cardinality constraints for the number of allowed occurrences of a property. Shapes can be combined using Boolean operators, and can use possibly recursive references to other shapes. We describe the syntax of the language and define its semantics. The semantics is proven to be well-defined for schemas that satisfy a reasonable syntactic restriction, namely stratified use of negation and recursion. We present two algorithms for the validation of an RDF graph against a shapes schema. The first algorithm is a direct implementation of the semantics, whereas the second is a non-trivial improvement. We also briefly give implementation guidelines.
Principles of Antifragile Software
Venue: arXiv cs.SE 2017
Year: 2017

The goal of this paper is to study and define the concept of "antifragile software". For this, I start from Taleb's statement that antifragile systems love errors, and discuss whether traditional software dependability fits into this class. The answer is somewhat negative, although adaptive fault tolerance is antifragile: the system learns something when an error happens, and always imrpoves. Automatic runtime bug fixing is changing the code in response to errors, fault injection in production means injecting errors in business critical software. I claim that both correspond to antifragility. Finally, I hypothesize that antifragile development processes are better at producing antifragile software systems.
Equilibrium Refinement through Negotiation in Binary Voting
Venue: arXiv cs.GT 2017
Year: 2017

We study voting games on binary issues, where voters hold an objective over the outcome of the collective decision and are allowed, before the vote takes place, to negotiate their voting strategy with the other participants. We analyse the voters' rational behaviour in the resulting two-phase game, showing under what conditions undesirable equilibria can be removed and desirable ones sustained as a consequence of the pre-vote phase.
A Low-Complexity Graph-Based LMMSE Receiver for MIMO ISI Channels with M-QAM Modulation
Venue: arXiv cs.IT 2017
Year: 2017

In this paper, we propose a low complexity graph-based linear minimum mean square error (LMMSE) equalizer in order to remove inter-symbol and inter-stream interference in multiple input multiple output (MIMO) communication. The proposed state space representation inflicted on the graph provides linearly increasing computational complexity with block length. Also, owing to the Gaussian assumption used in the presented cycle-free factor graph, the complexity of the suggested equalizer structure is not affected by the size of the signalling space. In addition, we introduce an efficient way of computing extrinsic bit log-likelihood ratio (LLR) values for LMMSE estimation compatible with higher order alphabets which is shown to perform better than the other methods in the literature. Overall, we provide an efficient receiver structure reaching high data rates in frequency selective MIMO systems whose performance is shown to be very close to a genie-aided matched filter bound through extensive simulations.
Static Analysis for Regular Expression Exponential Runtime via Substructural Logics (Extended)
Venue: arXiv cs.PL 2017
Year: 2017

Regular expression matching using backtracking can have exponential runtime, leading to an algorithmic complexity attack known as REDoS in the systems security literature. In this paper, we build on a recently published static analysis that detects whether a given regular expression can have exponential runtime for some inputs. We systematically construct a more accurate analysis by forming powers and products of transition relations and thereby reducing the REDoS problem to reachability. The correctness of the analysis is proved using a substructural calculus of search trees, where the branching of the tree causing exponential blowup is characterized as a form of non-linearity.
(k,l)-Unambiguity and Quasi-Deterministic Structures
Venue: arXiv cs.FL 2017
Year: 2017

We focus on the family of $(k,l)$-unambiguous automata that encompasses the one of deterministic $k$-lookahead automata introduced by Han and Wood. We show that this family presents nice theoretical properties that allow us to compute quasi-deterministic structures. These structures are smaller than DFAs and can be used to solve the membership problem faster than NFAs.
Maximum Likelihood Estimation of Functionals of Discrete Distributions
Venue: arXiv cs.IT 2017
Year: 2017

We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random fluctuation of these estimators around their expectations, and the theory of approximation using positive linear operators to analyze the deviation of their expectations from the true functional, namely their \emph{bias}. We characterize the worst case squared error risk incurred by the Maximum Likelihood Estimator (MLE) in estimating the Shannon entropy $H(P) = \sum_{i = 1}^S -p_i \ln p_i$, and $F_α(P) = \sum_{i = 1}^S p_i^α,α>0$, up to multiplicative constants, for any alphabet size $S\leq \infty$ and sample size $n$ for which the risk may vanish. As a corollary, for Shannon entropy estimation, we show that it is necessary and sufficient to have $n \gg S$ observations for the MLE to be consistent. In addition, we establish that it is necessary and sufficient to consider $n \gg S^{1/α}$ samples for the MLE to consistently estimate $F_α(P), 0<α<1$. The minimax rate-optimal estimators for both problems require $S/\ln S$ and $S^{1/α}/\ln S$ samples, which implies that the MLE has a strictly sub-optimal sample complexity. When $1<α<3/2$, we show that the worst-case squared error rate of convergence for the MLE is $n^{-2(α-1)}$ for infinite alphabet size, while the minimax squared error rate is $(n\ln n)^{-2(α-1)}$. When $α\geq 3/2$, the MLE achieves the minimax optimal rate $n^{-1}$ regardless of the alphabet size. As an application of the general theory, we analyze the Dirichlet prior smoothing techniques for Shannon entropy estimation. We show that no matter how we tune the parameters in the Dirichlet prior, this technique cannot achieve the minimax rates in entropy estimation.
Identifying codes in hereditary classes of graphs and VC-dimension
Venue: arXiv cs.DM 2017
Year: 2017

An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We show a dichotomy for the size of the smallest identifying code in classes of graphs closed under induced subgraphs. Our dichotomy is derived from the VC-dimension of the considered class C, that is the maximum VC-dimension over the hypergraphs formed by the closed neighbourhoods of elements of C. We show that hereditary classes with infinite VC-dimension have infinitely many graphs with an identifying code of size logarithmic in the number of vertices while classes with finite VC-dimension have a polynomial lower bound. We then turn to approximation algorithms. We show that the problem of finding a smallest identifying code in a given graph from some class is log-APX-hard for any hereditary class of infinite VC-dimension. For hereditary classes of finite VC-dimension, the only known previous results show that we can approximate the identifying code problem within a constant factor in some particular classes, e.g. line graphs, planar graphs and unit interval graphs. We prove that it can be approximate within a factor 6 for interval graphs. In contrast, we show that on C_4-free bipartite graphs (a class of finite VC-dimension) it cannot be approximated to within a factor of c.log(|V|) for some c>0.
PhaseCode: Fast and Efficient Compressive Phase Retrieval based on Sparse-Graph-Codes
Venue: arXiv cs.IT 2017
Year: 2017

We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of the $K$ non-zero signal components using only slightly more than $4K$ measurements when the support of the signal is uniformly random, with order-optimal time and memory complexity of $Θ(K)$. It is known that the fundamental limit for the number of measurements in compressive phase retrieval problem is $4K - o(K)$ to recover the signal exactly and with no assumptions on its support distribution. This shows that under mild relaxation of the conditions, our algorithm is the first constructive \emph{capacity-approaching} compressive phase retrieval algorithm: in fact, our algorithm is also order-optimal in complexity and memory. Next, motivated by some important practical classes of optical systems, we consider a Fourier-friendly constrained measurement setting, and show that its performance matches that of the unconstrained setting. In the Fourier-friendly setting that we consider, the measurement matrix is constrained to be a cascade of Fourier matrices and diagonal matrices. We further demonstrate how PhaseCode can be robustified to noise. Throughout, we provide extensive simulation results that validate the practical power of our proposed algorithms for the sparse unconstrained and Fourier-friendly measurement settings, for noiseless and noisy scenarios. A key contribution of our work is the novel use of coding-theoretic tools like density evolution methods for the design and analysis of fast and efficient algorithms for compressive phase-retrieval problems.
Homomorphism reconfiguration via homotopy
Venue: arXiv cs.CC 2017
Year: 2017

We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring throughout. This is the same as finding a path in the Hom(G,H) complex. For H=K_k this is the problem of finding paths between k-colorings, which was shown to be in P for k<=3 and PSPACE-complete otherwise by Cereceda et al. 2011. We generalize the positive side of this dichotomy by providing an algorithm that solves the problem in polynomial time for any H with no C_4 subgraph. This gives a large class of constraints for which finding solutions to the Constraint Satisfaction Problem is NP-complete, but finding paths in the solution space is P. The algorithm uses a characterization of possible reconfiguration sequences (paths in Hom(G,H)), whose main part is a purely topological condition described in algebraic terms of the fundamental groupoid of H seen as a topological space.
Towards crowdsourcing and cooperation in linguistic resources
Venue: arXiv cs.SI 2017
Year: 2017

Linguistic resources can be populated with data through the use of such approaches as crowdsourcing and gamification when motivated people are involved. However, current crowdsourcing genre taxonomies lack the concept of cooperation, which is the principal element of modern video games and may potentially drive the annotators' interest. This survey on crowdsourcing taxonomies and cooperation in linguistic resources provides recommendations on using cooperation in existent genres of crowdsourcing and an evidence of the efficiency of cooperation using a popular Russian linguistic resource created through crowdsourcing as an example.
A Linear Kernel for Planar Red-Blue Dominating Set
Venue: arXiv cs.DS 2017
Year: 2017

In the Red-Blue Dominating Set problem, we are given a bipartite graph $G = (V_B \cup V_R,E)$ and an integer $k$, and asked whether $G$ has a subset $D \subseteq V_B$ of at most $k$ "blue" vertices such that each "red" vertex from $V_R$ is adjacent to a vertex in $D$. We provide the first explicit linear kernel for this problem on planar graphs, of size at most $43k$.
Hyperbolicity, degeneracy, and expansion of random intersection graphs
Venue: arXiv cs.SI 2017
Year: 2017

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we fully characterize the degeneracy of random intersection graphs, and prove that the model asymptotically almost surely produces graphs with hyperbolicity at least $\log{n}$. Further, we prove that in the parametric regime where random intersection graphs are degenerate an even stronger notion of sparseness, so called bounded expansion, holds with high probability. We supplement our theoretical findings with experimental evaluations of the relevant statistics.
A Characterization for Decidable Separability by Piecewise Testable Languages
Venue: arXiv cs.FL 2017
Year: 2017

The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes $I$ and excludes $E$, that is, $I \subseteq S$ and $S\cap E = \emptyset$. In this work, we assume some mild closure properties for $\mathcal{C}$ and study for which such classes separability by a piecewise testable language (PTL) is decidable. We characterize these classes in terms of decidability of (two variants of) an unboundedness problem. From this, we deduce that separability by PTL is decidable for a number of language classes, such as the context-free languages and languages of labeled vector addition systems. Furthermore, it follows that separability by PTL is decidable if and only if one can compute for any language of the class its downward closure wrt. the scattered substring ordering (i.e., if the set of scattered substrings of any language of the class is effectively regular). The obtained decidability results contrast some undecidability results. In fact, for all (non-regular) language classes that we present as examples with decidable separability, it is undecidable whether a given language is a PTL itself. Our characterization involves a result of independent interest, which states that for any kind of languages $I$ and $E$, non-separability by PTL is equivalent to the existence of common patterns in $I$ and $E$.
Asymptotically Optimum Perfect Universal Steganography of Finite Memoryless Sources
Venue: arXiv cs.IT 2017
Year: 2017

A solution to the problem of asymptotically optimum perfect universal steganography of finite memoryless sources with a passive warden is provided, which is then extended to contemplate a distortion constraint. The solution rests on the fact that Slepian's Variant I permutation coding implements first-order perfect universal steganography of finite host signals with optimum embedding rate. The duality between perfect universal steganography with asymptotically optimum embedding rate and lossless universal source coding with asymptotically optimum compression rate is evinced in practice by showing that permutation coding can be implemented by means of adaptive arithmetic coding. Next, a distortion constraint between the host signal and the information-carrying signal is considered. Such a constraint is essential whenever real-world host signals with memory (e.g., images, audio, or video) are decorrelated to conform to the memoryless assumption. The constrained version of the problem requires trading off embedding rate and distortion. Partitioned permutation coding is shown to be a practical way to implement this trade-off, performing close to an unattainable upper bound on the rate-distortion function of the problem.
A Spectral Assignment Approach for the Graph Isomorphism Problem
Venue: arXiv cs.DM 2017
Year: 2017

In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can be isospectral but non-isomorphic. We first construct a graph isomorphism testing algorithm for friendly graphs and then extend it to unambiguous graphs. We show that isomorphisms can be detected by solving a linear assignment problem. If the graphs possess repeated eigenvalues, which typically correspond to graph symmetries, finding isomorphisms is much harder. By repeatedly perturbing the adjacency matrices and by using properties of eigenpolytopes, it is possible to break symmetries of the graphs and iteratively assign vertices of $ G_A $ to vertices of $ G_B $, provided that an admissible assignment exists. This heuristic approach can be used to construct a permutation which transforms $ G_A $ into $ G_B $ if the graphs are isomorphic. The methods will be illustrated with several guiding examples.