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Lower Bounds for Adversarially Robust PAC LearningJun 13 2019In this work, we initiate a formal study of probably approximately correct (PAC) learning under evasion attacks, where the adversary's goal is to \emph{misclassify} the adversarially perturbed sample point $\widetilde{x}$, i.e., $h(\widetilde{x})\neq ... More

Querying a Matrix through Matrix-Vector ProductsJun 13 2019We consider algorithms with access to an unknown matrix $M\in\mathbb{F}^{n \times d}$ via matrix-vector products, namely, the algorithm chooses vectors $\mathbf{v}^1, \ldots, \mathbf{v}^q$, and observes $M\mathbf{v}^1,\ldots, M\mathbf{v}^q$. Here the ... More

A Turing Kernelization Dichotomy for Structural Parameterizations of $\mathcal{F}$-Minor-Free DeletionJun 13 2019For a fixed finite family of graphs $\mathcal{F}$, the $\mathcal{F}$-Minor-Free Deletion problem takes as input a graph $G$ and an integer $\ell$ and asks whether there exists a set $X \subseteq V(G)$ of size at most $\ell$ such that $G-X$ is $\mathcal{F}$-minor-free. ... More

Fixed-Parameter Tractability of Graph Deletion Problems over Data StreamsJun 13 2019In this work, we initiate a systematic study of parameterized streaming complexity of graph deletion problems: ${\cal F}$-Subgraph Deletion, ${\cal F}$-Minor Deletion and Cluster Vertex Deletion in the four most well-studied streaming models: the EA (edge ... More

The Tandem Duplication Distance is NP-hardJun 12 2019In computational biology, tandem duplication is an important biological phenomenon which can occur either at the genome or at the DNA level. A tandem duplication takes a copy of a genome segment and inserts it right after the segment - this can be represented ... More

Approximating the Orthogonality Dimension of Graphs and HypergraphsJun 12 2019A $t$-dimensional orthogonal representation of a hypergraph is an assignment of nonzero vectors in $\mathbb{R}^t$ to its vertices, such that every hyperedge contains two vertices whose vectors are orthogonal. The orthogonality dimension of a hypergraph ... More

Efficient Graph RewritingJun 11 2019Graph transformation is the rule-based modification of graphs, and is a discipline dating back to the 1970s. The declarative nature of graph rewriting rules comes at a cost. In general, to match the left-hand graph of a fixed rule within a host graph ... More

Efficiently escaping saddle points on manifoldsJun 10 2019Smooth, non-convex optimization problems on Riemannian manifolds occur in machine learning as a result of orthonormality, rank or positivity constraints. First- and second-order necessary optimality conditions state that the Riemannian gradient must be ... More

The Demand Query Model for Bipartite MatchingJun 10 2019We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching seem to be ... More

Complexity phase diagram for interacting and long-range bosonic HamiltoniansJun 10 2019Recent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity ... More

Coin Theorems and the Fourier ExpansionJun 10 2019In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and the norms of ... More

The Packed Interval Covering Problem is NP-completeJun 09 2019We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.

On the distribution of runners on a circleJun 06 2019Consider $n$ runners running on a circular track of unit length with constant speeds such that $k$ of the speeds are distinct. We show that, at some time, there will exist a sector $S$ which contains at least $|S|n+ \Omega(\sqrt{k})$ runners. The result ... More

On the computability properties of topological entropy: a general approachJun 04 2019The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological entropy for this ... More

Learning dynamic polynomial proofsJun 04 2019Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of semi-algebraic proof systems ... More

Quasi-automatic groups are asynchronously automaticJun 04 2019A quasi-automatic semigroup is a finitely generated semigroup with a rational set of representatives such that the graph of right multiplication by any generator is a rational relation. A asynchronously automatic semigroup is a quasi-automatic semigroup ... More

A deterministic algorithm for counting colorings with $2Δ$ colorsJun 04 2019Jun 06 2019We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting the number of $q$-colorings of a graph of maximum degree $\Delta$, provided only that $q\ge 2\Delta$. This substantially improves on previous deterministic algorithms ... More

A deterministic algorithm for counting colorings with $2Δ$ colorsJun 04 2019We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting the number of $q$-colorings of a graph of maximum degree $\Delta$, provided only that $q\ge 2\Delta$. This substantially improves on previous deterministic algorithms ... More

Phase-based Minimalist Parsing and complexity in non-local dependenciesJun 03 2019A cognitively plausible parsing algorithm should perform like the human parser in critical contexts. Here I propose an adaptation of Earley's parsing algorithm, suitable for Phase-based Minimalist Grammars (PMG, Chesi 2012), that is able to predict complexity ... More

Parameterised Complexity for AbductionJun 03 2019Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version asking for sets of variables as explanations, we study, ... More

Multistage Vertex CoverJun 03 2019Covering all edges of a graph by a minimum number of vertices, this is the NP-hard Vertex Cover problem, is among the most fundamental algorithmic tasks. Following a recent trend in studying dynamic and temporal graphs, we initiate the study of Multistage ... More

Approximate degree, secret sharing, and concentration phenomenaJun 02 2019The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there exists a pair of ... More

Ubiquitous Complexity of Entanglement SpectraJun 02 2019In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking phases, and eigenstate ... More

On the computational complexity of the probabilistic label tree algorithmsJun 01 2019Label tree-based algorithms are widely used to tackle multi-class and multi-label problems with a large number of labels. We focus on a particular subclass of these algorithms that use probabilistic classifiers in the tree nodes. Examples of such algorithms ... More

Probabilistic Top-k Dominating Query Monitoring over Multiple Uncertain IoT Data Streams in Edge Computing EnvironmentsJun 01 2019Extracting the valuable features and information in Big Data has become one of the important research issues in Data Science. In most Internet of Things (IoT) applications, the collected data are uncertain and imprecise due to sensor device variations ... More

On the Acceleration of the Sinkhorn and Greenkhorn Algorithms for Optimal TransportJun 01 2019We propose and analyze a novel approach to accelerate the Sinkhorn and Greenkhorn algorithms for solving the entropic regularized optimal transport (OT) problems. Focusing on the discrete setting where the probability distributions have at most $n$ atoms, ... More

Human-Usable Password Schemas: Beyond Information-Theoretic SecurityMay 31 2019Password users frequently employ passwords that are too simple, or they just reuse passwords for multiple websites. A common complaint is that utilizing secure passwords is too difficult. One possible solution to this problem is to use a password schema. ... More

Data Complexity and Rewritability of Ontology-Mediated Queries in Metric Temporal Logic under the Event-Based Semantics (Full Version)May 30 2019We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions. We identify classes of ontology-mediated ... More

Consistency of circuit lower bounds with bounded theoriesMay 30 2019Proving that there are problems in $\mathsf{P}^\mathsf{NP}$ that require boolean circuits of super-linear size is a major frontier in complexity theory. While such lower bounds are known for larger complexity classes, existing results only show that the ... More

Resolution Lower Bounds for Refutation StatementsMay 29 2019For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in (Atserias, M\"uller ... More

Complexity lower bounds for computing the approximately-commuting operator value of non-local games to high precisionMay 28 2019We study the problem of approximating the commuting-operator value of a two-player non-local game. It is well-known that it is $\mathrm{NP}$-complete to decide whether the classical value of a non-local game is 1 or $1- \epsilon$. Furthermore, as long ... More

Average Bias and Polynomial SourcesMay 28 2019We identify a new notion of pseudorandomness for randomness sources, which we call the average bias. Given a distribution $Z$ over $\{0,1\}^n$, its average bias is: $b_{\text{av}}(Z) =2^{-n} \sum_{c \in \{0,1\}^n} |\mathbb{E}_{z \sim Z}(-1)^{\langle c, ... More

Average Bias and Polynomial SourcesMay 28 2019May 30 2019We identify a new notion of pseudorandomness for randomness sources, which we call the average bias. Given a distribution $Z$ over $\{0,1\}^n$, its average bias is: $b_{\text{av}}(Z) =2^{-n} \sum_{c \in \{0,1\}^n} |\mathbb{E}_{z \sim Z}(-1)^{\langle c, ... More

Adversarially Robust Learning Could Leverage Computational HardnessMay 28 2019Over recent years, devising classification algorithms that are robust to adversarial perturbations has emerged as a challenging problem. In particular, deep neural nets (DNNs) seem to be susceptible to small imperceptible changes over test instances. ... More

Noise sensitivity of Boson Sampling and density of bosonsMay 27 2019Inevitable experimental noise lies on the way to demonstrate the computational advantage of quantum devices over digital computers in some specific tasks. One of the proposals is Boson Sampling of Aaronson & Arkhipov, where the specific classically hard ... More

Perfect zero knowledge for quantum multiprover interactive proofsMay 27 2019In this work we consider the interplay between multiprover interactive proofs, quantum entanglement, and zero knowledge proofs - notions that are central pillars of complexity theory, quantum information and cryptography. In particular, we study the relationship ... More

Hierarchy of Transportation Network Parameters and Hardness ResultsMay 27 2019The graph parameters highway dimension and skeleton dimension were introduced to capture the properties of transportation networks. As many important optimization problems like Travelling Salesperson, Steiner Tree or $k$-Center arise in such networks, ... More

A Rate-Distortion Framework for Explaining Neural Network DecisionsMay 27 2019We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected classifier score remains ... More

Regular resolution for CNF of bounded incidence treewidth with few long clausesMay 26 2019We demonstrate that Regular Resolution is FPT for two restricted families of CNFs of bounded incidence treewidth. The first includes CNFs having at most $p$ clauses whose removal results in a CNF of primal treewidth at most $k$. The parameters we use ... More

On the monotone complexity of the shift operatorMay 26 2019We show that the complexity of minimal monotone circuits implementing a monotone version of the shift operator on $n$ boolean inputs is $\Theta(n\log n)$.

Counting Homomorphisms Modulo a Prime NumberMay 25 2019Counting problems in general and counting graph homomorphisms in particular have numerous applications in combinatorics, computer science, statistical physics, and elsewhere. One of the most well studied problems in this area is #GraphHom(H) --- the problem ... More

Computational cost for determining an approximate global minimum using the selection and crossover algorithmMay 24 2019This work examines the expected computational cost to determine an approximate global minimum of a class of cost functions characterized by the variance of coefficients. The cost function takes $N$-dimensional binary states as arguments and has many local ... More

Optimum Low-Complexity Decoder for Spatial ModulationMay 22 2019In this paper, a novel low-complexity detection algorithm for spatial modulation (SM), referred to as the minimum-distance of maximum-length (m-M) algorithm, is proposed and analyzed. The proposed m-M algorithm is a smart searching method that is applied ... More

Solving Random Systems of Quadratic Equations with Tanh Wirtinger FlowMay 22 2019Solving quadratic systems of equations in n variables and m measurements of the form $y_i = |a^T_i x|^2$ , $i = 1, ..., m$ and $x \in R^n$ , which is also known as phase retrieval, is a hard nonconvex problem. In the case of standard Gaussian measurement ... More

The Computational Complexity of Understanding Network DecisionsMay 22 2019For a Boolean function $\Phi\colon\{0,1\}^d\to\{0,1\}$ and an assignment to its variables $\mathbf{x}=(x_1, x_2, \dots, x_d)$ we consider the problem of finding the subsets of the variables that are sufficient to determine the function value with a given ... More

Shortest-Path-Preserving RoundingMay 21 2019Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be preferable ... More

Subcubic Equivalences Between Graph Centrality Measures and Complementary ProblemsMay 20 2019Despite persistent efforts, there is no known technique for obtaining unconditional super-linear lower bounds for the computational complexity of the problems in P. Vassilevska Williams and Williams introduce a fruitful approach to advance a better understanding ... More

Broadcast Congested Clique: Planted Cliques and Pseudorandom GeneratorsMay 19 2019We develop techniques to prove lower bounds for the BCAST(log n) Broadcast Congested Clique model (a distributed message passing model where in each round, each processor can broadcast an O(log n)-sized message to all other processors). Our techniques ... More

Lasserre Integrality Gaps for Graph Spanners and Related ProblemsMay 17 2019There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a given input graph. Essentially all of these algorithms use the same basic LP relaxation, so a variety ... More

Shortest Path Algorithms between Theory and PracticeMay 17 2019Utilizing graph algorithms is a common activity in computer science. Algorithms that perform computations on large graphs are not always efficient. This work investigates the Single-Source Shortest Path (SSSP) problem, which is considered to be one of ... More

Separating k-Player from t-Player One-Way Communication, with Applications to Data StreamsMay 17 2019In a $k$-party communication problem, the $k$ players with inputs $x_1, x_2, \ldots, x_k$, respectively, want to evaluate a function $f(x_1, x_2, \ldots, x_k)$ using as little communication as possible. We consider the message-passing model, in which ... More

Parameterized Inapproximability of Exact Cover and Nearest CodewordMay 16 2019The $k$-ExactCover problem is a parameterized version of the ExactCover problem, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and an integer $k$, and the task is to determine whether $U$ can be partitioned into $k$ sets in ... More

Parameterized Inapproximability of Exact Cover and Nearest CodewordMay 16 2019May 18 2019The $k$-ExactCover problem is a parameterized version of the ExactCover problem, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and an integer $k$, and the task is to determine whether $U$ can be partitioned into $k$ sets in ... More

Quantum Complexity of Time Evolution with Chaotic HamiltoniansMay 14 2019We study the quantum complexity of time evolution in large-$N$ chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the ... More

Stochastic thermodynamics of computationMay 14 2019One of the major resource requirements of computers - ranging from biological cells to human brains to high-performance (engineered) computers - is the energy used to run them. Those costs of performing a computation have long been a focus of research ... More

Generating Weighted MAX-2-SAT Instances of Tunable Difficulty with Frustrated LoopsMay 14 2019Many optimization problems can be cast into the maximum satisfiability (MAX-SAT) form, and many solvers have been developed for tackling such problems. To evaluate the performance of a MAX-SAT solver, it is convenient to generate difficult MAX-SAT instances ... More

Computing Maximum Matchings in Temporal GraphsMay 13 2019We study the computational complexity of finding maximum-cardinality temporal matchings in temporal graphs (where the edge set may change over time while the vertex set remains fixed). Our model of temporal matching (which seems to be slightly more general ... More

About a certain NP complete problemMay 13 2019In this article, we introduce the concept of special decomposition of a set under the given pairs of subsets of that set, and the concept of special covering of a set under such a decomposition. We study the conditions for existence of special coverings ... More

On Semigroups of Two-Dimensional Upper-Triangular Integer MatricesMay 13 2019We analyze algorithmic problems in finitely generated semigroups of two-dimensional upper-triangular integer matrices. These semigroup problems are tightly connected with problems about compositions of affine functions over one variable. Building on a ... More

Orthogonal tensor decomposition and orbit closures from a linear algebraic perspectiveMay 13 2019We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new proof of some ... More

Satisfiability Threshold for Power Law Random 2-SAT in Configuration ModelMay 13 2019The Random Satisfiability problem has been intensively studied for decades. For a number of reasons the focus of this study has mostly been on the model, in which instances are sampled uniformly at random from a set of formulas satisfying some clear conditions, ... More

Complexity of fall coloring for restricted graph classesMay 12 2019We strengthen a result by Laskar and Lyle (Discrete Appl. Math. (2009), 330-338) by proving that it is NP-complete to decide whether a bipartite planar graph can be partitioned into three independent dominating sets. In contrast, we show that this is ... More

Continuous-Time Systems for Solving 0-1 Integer Linear Programming Feasibility ProblemsMay 12 2019The 0-1 integer linear programming feasibility problem is an important NP-complete problem. This paper proposes a continuous-time dynamical system for solving that problem without getting trapped in non-solution local minima. First, the problem is transformed ... More

Seeding with Costly Network InformationMay 10 2019The spread of behavior over social networks depends on the contact structure among individuals, and seeding the most influential agents can substantially enhance the extent of the spread. While the choice of the best seed set, known as influence maximization, ... More

Online Multistage Subset Maximization ProblemsMay 10 2019Numerous combinatorial optimization problems (knapsack, maximum-weight matching, etc.) can be expressed as \emph{subset maximization problems}: One is given a ground set $N=\{1,\dots,n\}$, a collection $\mathcal{F}\subseteq 2^N$ of subsets thereof such ... More

Elimination Distances, Blocking Sets, and Kernels for Vertex CoverMay 09 2019The Vertex Cover problem plays an essential role in the study of polynomial kernelization in parameterized complexity, i.e., the study of provable and efficient preprocessing for NP-hard problems. Motivated by the great variety of positive and negative ... More

Revisiting Graph Width Measures for CNF-EncodingsMay 09 2019We consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied for their uses ... More

The asymptotic induced matching number of hypergraphs: balanced binary stringsMay 08 2019We compute the asymptotic induced matching number of the $k$-partite $k$-uniform hypergraphs whose edges are the $k$-bit strings of Hamming weight $k/2$, for any large enough even number $k$. Our lower bound relies on the higher-order extension of the ... More

Finding cuts of bounded degree: complexity, FPT and exact algorithms, and kernelizationMay 08 2019A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been intensively ... More

Key-agreement based on automaton groupsMay 08 2019We suggest several automaton groups as key-agreement platforms for Anshl-Anshel-Goldfeld metascheme, they include Grigorchuk and universal Grigorchuk groups, Hanoi 3-Towers group, Basilica group and a subgroup of the affine group with the unsolvable conjugacy ... More

The algorithm for the recovery of integer vector via linear measurementsMay 07 2019In this paper we continue the studies on the integer sparse recovery problem that was introduced in \cite{FKS} and studied in \cite{K},\cite{KS}. We provide an algorithm for the recovery of an unknown sparse integer vector for the measurement matrix described ... More

Lifted Multiplicity CodesMay 06 2019Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We generalize their construction ... More

Lifted multiplicity codes and the disjoint repair group propertyMay 06 2019Jun 12 2019Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We consider a generalization ... More

Incorporating Weisfeiler-Leman into algorithms for group isomorphismMay 06 2019In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show how to combine ... More

FPT Algorithms for Conflict-free Coloring of Graphs and Chromatic Terrain GuardingMay 06 2019We present fixed parameter tractable algorithms for the conflict-free coloring problem on graphs. Given a graph $G=(V,E)$, \emph{conflict-free coloring} of $G$ refers to coloring a subset of $V$ such that for every vertex $v$, there is a color that is ... More

Space-bounded Church-Turing thesis and computational tractability of closed systemsMay 02 2019We report a new limitation on the ability of physical systems to perform computation -- one that is based on generalizing the notion of memory, or storage space, available to the system to perform the computation. Roughly, we define memory as the maximal ... More

Establishing the Quantum Supremacy Frontier with a 281 Pflop/s SimulationMay 01 2019Noisy Intermediate-Scale Quantum (NISQ) computers aim to perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires ... More

Parameterized Complexity of Conflict-free Graph ColoringMay 01 2019Given a graph G, a q-open neighborhood conflict-free coloring or q-ONCF-coloring is a vertex coloring $c:V(G) \rightarrow \{1,2,\ldots,q\}$ such that for each vertex $v \in V(G)$ there is a vertex in $N(v)$ that is uniquely colored from the rest of the ... More

On a conditional inequality in Kolmogorov complexity and its applications in communication complexityMay 01 2019Romashchenko and Zimand~\cite{rom-zim:c:mutualinfo} have shown that if we partition the set of pairs $(x,y)$ of $n$-bit strings into combinatorial rectangles, then $I(x:y) \geq I(x:y \mid t(x,y)) - O(\log n)$, where $I$ denotes mutual information in the ... More

Derandomization from Algebraic Hardness: Treading the BordersApr 30 2019A hitting-set generator (HSG) is a polynomial map $Gen:\mathbb{F}^k \to \mathbb{F}^n$ such that for all $n$-variate polynomials $Q$ of small enough circuit size and degree, if $Q$ is non-zero, then $Q\circ Gen$ is non-zero. In this paper, we give a new ... More

Constrained Orthogonal Segment StabbingApr 30 2019Let $S$ and $D$ each be a set of orthogonal line segments in the plane. A line segment $s\in S$ \emph{stabs} a line segment $s'\in D$ if $s\cap s'\neq\emptyset$. It is known that the problem of stabbing the line segments in $D$ with the minimum number ... More

Case Study of the Proof of Cook's theorem - Interpretation of A(w)Apr 30 2019Cook's theorem is commonly expressed such as any polynomial time-verifiable problem can be reduced to the SAT problem. The proof of Cook's theorem consists in constructing a propositional formula A(w) to simulate a computation of TM, and such A(w) is ... More

Query-to-communication lifting for BPP using inner productApr 30 2019We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic ... More

The Littlewood-Offord Problem for Markov ChainsApr 30 2019The celebrated Littlewood-Offord problem asks for an upper bound on the probability that the random variable $\epsilon_1 v_1 + \cdots + \epsilon_n v_n$ lies in the Euclidean unit ball, where $\epsilon_1, \ldots, \epsilon_n \in \{-1, 1\}$ are independent ... More

Testing tensor productsApr 29 2019A function $f:[n]^d\to\mathbb{F}_2$ is a direct sum if it is of the form $ f\left((a_1,\dots,a_d)\right) = f_1(a_1)+\dots + f_d (a_d),$ for some $d$ functions $f_1,\dots,f_d:[n]\to\mathbb{F}_2$. We present a $4$-query test which distinguishes between ... More

A Complete Classification of the Complexity and Rewritability of Ontology-Mediated Queries based on the Description Logic ELApr 29 2019We provide an ultimately fine-grained analysis of the data complexity and rewritability of ontology-mediated queries (OMQs) based on an EL ontology and a conjunctive query (CQ). Our main results are that every such OMQ is in AC0, NL-complete, or PTime-complete ... More

Solving Vertex Cover in Polynomial Time on Hyperbolic Random GraphsApr 29 2019The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world ... More

Dichotomy for symmetric Boolean PCSPsApr 29 2019A PCSP is a combination of two CSPs defined by two similar templates; the computational question is to distinguish a YES instance of the first one from a NO instance of the second. The computational complexity of many PCSPs remains unknown. Even the case ... More

Efficient Black-Box Identity Testing over Free Group AlgebraApr 28 2019Hrube\v{s} and Wigderson [HW14] initiated the study of noncommutative arithmetic circuits with division computing a noncommutative rational function in the free skew field, and raised the question of rational identity testing. It is now known that the ... More

Blended Matching PursuitApr 28 2019Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for minimizing a ... More

Parameterised Counting Classes with Bounded NondeterminismApr 27 2019Stockhusen and Tantau (IPEC 2013) introduced the operators paraW and paraBeta for parameterised space complexity classes by allowing bounded nondeterminism with read-only and read-once access, respectively. Using these operators, they could characterise ... More

A Note on Computational Complexity of Dou Shou QiApr 27 2019Dou Shou Qi is a Chinese strategy board game for two players. We use a EXPTIME-hardness framework to analyse computational complexity of the game. We construct all gadgets of the hardness framework. In conclusion, we prove that Dou Shou Qi is EXPTIME-complete. ... More

On the Complexity of Local Graph TransformationsApr 25 2019We consider the problem of transforming a given graph $G_s$ into a desired graph $G_t$ by applying a minimum number primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each node can apply ... More

Detecting and Counting Small Patterns in Planar Graphs in Subexponential Parameterized TimeApr 25 2019We present an algorithm that takes as input an $n$-vertex planar graph $G$ and a $k$-vertex pattern graph $P$, and computes the number of (induced) copies of $P$ in $G$ in $2^{O(k/\log k)}n^{O(1)}$ time. If $P$ is a matching, independent set, or connected ... More

Normalizers and permutational isomorphisms in simply-exponential timeApr 24 2019We show that normalizers and permutational isomorphisms of permutation groups given by generating sets can be computed in time simply exponential in the degree of the groups. The result is obtained by exploiting canonical forms for permutation groups ... More

Counting perfect matchings and the eight-vertex modelApr 23 2019We study the approximation complexity of the partition function of the eight-vertex model on general 4-regular graphs. For the first time, we relate the approximability of the eight-vertex model to the complexity of approximately counting perfect matchings, ... More

Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardnessApr 23 2019We study the problem #IndSub(P) of counting all induced subgraphs of size k in a graph G that satisfy the property P. This problem was introduced by Jerrum and Meeks and shown to be #W[1]-hard when parameterized by k for some families of properties P ... More

Hierarchical b-MatchingApr 23 2019A matching of a graph is a subset of edges no two of which share a common vertex, and a maximum matching is a matching of maximum cardinality. In a $b$-matching every vertex $v$ has an associated bound $b_v$, and a maximum $b$-matching is a maximum set ... More

Computational Complexity of Restricted Diffusion Limited AggregationApr 22 2019We introduce a restricted version of the Diffusion Limited Aggregation (DLA) model. DLA is a cluster growth model that consists in series of particles that are thrown one by one from the top edge of a two (on more) dimensional grid, where they undergo ... More

Computational Complexity of Restricted Diffusion Limited AggregationApr 22 2019May 02 2019We introduce a restricted version of the Diffusion Limited Aggregation (DLA) model. DLA is a cluster growth model that consists in series of particles that are thrown one by one from the top edge of a two (on more) dimensional grid, where they undergo ... More