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  • (In)approximability of Maximum Minimal FVS
    arXiv.cs.CC Pub Date : 2020-09-21
    Louis Dublois; Tesshu Hanaka; Mehdi Khosravian Ghadikolaei; Michael Lampis; Nikolaos Melissinos

    We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type: \textsc{Maximum Minimal Vertex Cover}, for which the best achievable approximation ratio is $\sqrt{n}$, and \textsc{Upper Dominating Set}, which does not admit any $n^{1-\epsilon}$

    更新日期:2020-09-22
  • The Complexity of Constrained Min-Max Optimization
    arXiv.cs.CC Pub Date : 2020-09-21
    Constantinos Daskalakis; Stratis Skoulakis; Manolis Zampetakis

    Despite its important applications in Machine Learning, min-max optimization of nonconvex-nonconcave objectives remains elusive. Not only are there no known first-order methods converging even to approximate local min-max points, but the computational complexity of identifying them is also poorly understood. In this paper, we provide a characterization of the computational complexity of the problem

    更新日期:2020-09-22
  • Recent Progress on Matrix Rigidity -- A Survey
    arXiv.cs.CC Pub Date : 2020-09-20
    C. Ramya

    The concept of matrix rigidity was introduced by Valiant(independently by Grigoriev) in the context of computing linear transformations. A matrix is rigid if it is far(in terms of Hamming distance) from any matrix of low rank. Although we know rigid matrices exist, obtaining explicit constructions of rigid matrices have remained a long-standing open question. This decade has seen tremendous progress

    更新日期:2020-09-22
  • Answering Counting Queries over DL-Lite Ontologies
    arXiv.cs.CC Pub Date : 2020-09-02
    Meghyn BienvenuUB, CNRS, Bordeaux INP, LaBRI; Quentin ManièreUB, CNRS, Bordeaux INP, LaBRI; Michaël ThomazoVALDA

    Ontology-mediated query answering (OMQA) is a promising approach to data access and integration that has been actively studied in the knowledge representation and database communities for more than a decade. The vast majority of work on OMQA focuses on conjunctive queries, whereas more expressive queries that feature counting or other forms of aggregation remain largely unex-plored. In this paper,

    更新日期:2020-09-22
  • Directed branch-width: A directed analogue of tree-width
    arXiv.cs.CC Pub Date : 2020-09-18
    Benjamin Merlin Bumpus; Kitty Meeks; William Pettersson

    We introduce a new digraph width measure called directed branch-width. To do this, we generalize a characterization of graph classes of bounded tree-width in terms of their line graphs to digraphs. Under parameterizations by directed branch-width we obtain linear time algorithms for many problems, such as directed Hamilton path and Max-Cut, which are hard when parameterized by other known directed

    更新日期:2020-09-21
  • On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency
    arXiv.cs.CC Pub Date : 2020-09-17
    Ronny TredupUniversität Rostock; Evgeny ErofeevUniversität Oldenburg

    Modeling of real-world systems with Petri nets allows to benefit from their generic concepts of parallelism, synchronisation and conflict, and obtain a concise yet expressive system representation. Algorithms for synthesis of a net from a sequential specification enable the well-developed theory of Petri nets to be applied for the system analysis through a net model. The problem of $\tau$-synthesis

    更新日期:2020-09-21
  • ACSS-q: Algorithmic complexity for short strings via quantum accelerated approach
    arXiv.cs.CC Pub Date : 2020-09-18
    Aritra Sarkar; Koen Bertels

    In this research we present a quantum circuit for estimating algorithmic complexity using the coding theorem method. This accelerates inferring algorithmic structure in data for discovering causal generative models. The computation model is restricted in time and space resources to make it computable in approximating the target metrics. The quantum circuit design based on our earlier work that allows

    更新日期:2020-09-21
  • Hardness and approximation of the Probabilistic $p$-Center problem under Pressure
    arXiv.cs.CC Pub Date : 2020-09-18
    Marc Demange; Marcel A. Haddad; Cécile Murat

    The Probabilistic $p$-Center problem under Pressure ({\tt Min P$p$CP}) is a variant of the usual {\tt Min $p$-Center} problem we recently introduced in the context of wildfire management. The problem is %basically to locate $p$ shelters minimizing the maximum distance people will have to cover %in order to reach one of these shelters to reach the closest accessible shelter in case of fire. The landscape

    更新日期:2020-09-21
  • On the Tractability of SHAP Explanations
    arXiv.cs.CC Pub Date : 2020-09-18
    Guy Van den Broeck; Anton Lykov; Maximilian Schleich; Dan Suciu

    SHAP explanations are a popular feature-attribution mechanism for explainable AI. They use game-theoretic notions to measure the influence of individual features on the prediction of a machine learning model. Despite a lot of recent interest from both academia and industry, it is not known whether SHAP explanations of common machine learning models can be computed efficiently. In this paper, we establish

    更新日期:2020-09-21
  • Sparsification Lower Bounds for List $H$-Coloring
    arXiv.cs.CC Pub Date : 2020-09-17
    Hubie Chen; Bart M. P. Jansen; Karolina Okrasa; Astrid Pieterse; Paweł Rzążewski

    We investigate the List $H$-Coloring problem, the generalization of graph coloring that asks whether an input graph $G$ admits a homomorphism to the undirected graph $H$ (possibly with loops), such that each vertex $v \in V(G)$ is mapped to a vertex on its list $L(v) \subseteq V(H)$. An important result by Feder, Hell, and Huang [JGT 2003] states that List $H$-Coloring is polynomial-time solvable if

    更新日期:2020-09-20
  • Strongly refuting all semi-random Boolean CSPs
    arXiv.cs.CC Pub Date : 2020-09-17
    Jackson Abascal; Venkatesan Guruswami; Pravesh K. Kothari

    We give an efficient algorithm to strongly refute \emph{semi-random} instances of all Boolean constraint satisfaction problems. The number of constraints required by our algorithm matches (up to polylogarithmic factors) the best-known bounds for efficient refutation of fully random instances. Our main technical contribution is an algorithm to strongly refute semi-random instances of the Boolean $k$-XOR

    更新日期:2020-09-20
  • Improved Quantum Boosting
    arXiv.cs.CC Pub Date : 2020-09-17
    Adam Izdebski; Ronald de Wolf

    Boosting is a general method to convert a weak learner (which generates hypotheses that are just slightly better than random) into a strong learner (which generates hypotheses that are much better than random). Recently, Arunachalam and Maity gave the first quantum improvement for boosting, by combining Freund and Schapire's AdaBoost algorithm with a quantum algorithm for approximate counting. Their

    更新日期:2020-09-20
  • Tropical Kirchhoff's Formula and Postoptimality in Matroid Optimization
    arXiv.cs.CC Pub Date : 2020-09-16
    Stasys Jukna; Hannes Seiwert

    Given an assignment of real weights to the ground elements of a matroid, the min-max weight of a ground element $e$ is the minimum, over all circuits containing $e$, of the maximum weight of an element in that circuit with the element $e$ removed. We use this concept to answer the following structural questions for the minimum weight basis problem. Which elements are persistent under a given weighting

    更新日期:2020-09-17
  • Relaxed Locally Correctable Codes with Improved Parameters
    arXiv.cs.CC Pub Date : 2020-09-15
    Vahid R. Asadi; Igor Shinkar

    Locally decodable codes (LDCs) are error-correcting codes $C : \Sigma^k \to \Sigma^n$ that admit a local decoding algorithm that recovers each individual bit of the message by querying only a few bits from a noisy codeword. An important question in this line of research is to understand the optimal trade-off between the query complexity of LDCs and their block length. Despite importance of these objects

    更新日期:2020-09-17
  • Positivity-preserving extensions of sum-of-squares pseudomoments over the hypercube
    arXiv.cs.CC Pub Date : 2020-09-15
    Dmitriy Kunisky

    We introduce a new method for building higher-degree sum-of-squares lower bounds over the hypercube $\mathbf{x} \in \{\pm 1\}^N$ from a given degree 2 lower bound. Our method constructs pseudoexpectations that are positive semidefinite by design, lightening some of the technical challenges common to other approaches to SOS lower bounds, such as pseudocalibration. We give general "incoherence" conditions

    更新日期:2020-09-16
  • Statistical Query Algorithms and Low-Degree Tests Are Almost Equivalent
    arXiv.cs.CC Pub Date : 2020-09-13
    Matthew Brennan; Guy Bresler; Samuel B. Hopkins; Jerry Li; Tselil Schramm

    Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of computation, which on the one hand yields strong computational lower bounds for powerful classes of algorithms and on the other hand helps guide the development of efficient

    更新日期:2020-09-15
  • The Platform Design Problem
    arXiv.cs.CC Pub Date : 2020-09-13
    Christos Papadimitriou; Kiran Vodrahalli; Mihalis Yannakakis

    On-line firms deploy suites of software platforms, where each platform is designed to interact with users during a certain activity, such as browsing, chatting, socializing, emailing, driving, etc. The economic and incentive structure of this exchange, as well as its algorithmic nature, have not been explored to our knowledge; we initiate their study in this paper. We model this interaction as a Stackelberg

    更新日期:2020-09-15
  • Open Problem: Average-Case Hardness of Hypergraphic Planted Clique Detection
    arXiv.cs.CC Pub Date : 2020-09-12
    Yuetian Luo; Anru R. Zhang

    We note the significance of hypergraphic planted clique (HPC) detection in the investigation of computational hardness for a range of tensor problems. We ask if more evidence for the computational hardness of HPC detection can be developed. In particular, we conjecture if it is possible to establish the equivalence of the computational hardness between HPC and PC detection.

    更新日期:2020-09-15
  • Linear Shannon Capacity of Cayley Graphs
    arXiv.cs.CC Pub Date : 2020-09-11
    Venkatesan Guruswami; Andrii Riazanov

    The Shannon capacity of a graph is a fundamental quantity in zero-error information theory measuring the rate of growth of independent sets in graph powers. Despite being well-studied, this quantity continues to hold several mysteries. Lov\'asz famously proved that the Shannon capacity of $C_5$ (the 5-cycle) is at most $\sqrt{5}$ via his theta function. This bound is achieved by a simple linear code

    更新日期:2020-09-15
  • Explicit SoS lower bounds from high-dimensional expanders
    arXiv.cs.CC Pub Date : 2020-09-11
    Irit Dinur; Yuval Filmus; Prahladh Harsha; Madhur Tulsiani

    We construct an explicit family of 3XOR instances which is hard for $O(\sqrt{\log n})$ levels of the Sum-of-Squares hierarchy. In contrast to earlier constructions, which involve a random component, our systems can be constructed explicitly in deterministic polynomial time. Our construction is based on the high-dimensional expanders devised by Lubotzky, Samuels and Vishne, known as LSV complexes or

    更新日期:2020-09-14
  • Repeated Recursion Unfolding for Super-Linear Speedup within Bounds
    arXiv.cs.CC Pub Date : 2020-09-11
    Thom Fruehwirth

    Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of recursive rule applications to its logarithm at the expense of introducing a logarithmic number of unfolded rules to the program. Efficiency crucially depends on the

    更新日期:2020-09-14
  • Consensus under Network Interruption and Effective Resistance Interdiction
    arXiv.cs.CC Pub Date : 2020-09-11
    S. Rasoul Etesami

    We study the problem of network robustness under consensus dynamics. We first show that maximizing the consensus time subject to removing limited network edges can be cast as an effective resistance interdiction problem. We then show that the effective resistance interdiction problem is strongly NP-hard, even for three types of resistors in the network, hence correcting some claims in the existing

    更新日期:2020-09-14
  • Toward Probabilistic Checking against Non-Signaling Strategies with Constant Locality
    arXiv.cs.CC Pub Date : 2020-09-10
    Mohammad Mahdi Jahanara; Sajin Koroth; Igor Shinkar

    Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is probabilistically checkable proof

    更新日期:2020-09-11
  • Pushdown and Lempel-Ziv Depth
    arXiv.cs.CC Pub Date : 2020-09-10
    Liam Jordon; Philippe Moser

    This paper expands upon existing and introduces new formulations of Bennett's logical depth. In previously published work by Jordon and Moser, notions of finite-state-depth and pushdown-depth were examined and compared. These were based on finite-state transducers and information lossless pushdown compressors respectively. Unfortunately a full separation between the two notions was not established

    更新日期:2020-09-11
  • Completeness in Polylogarithmic Time and Space
    arXiv.cs.CC Pub Date : 2020-09-08
    Flavio Ferrarotti; Senen Gonzalez; Klaus-Dieter Schewe; Jose Maria Turull-Torres

    Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many natural algorithms resulting from current applications have polylogarithmic time (PolylogTime) or space complexity (PolylogSpace). The classical Karp notion of complete

    更新日期:2020-09-10
  • Combining Determinism and Non-Determinism
    arXiv.cs.CC Pub Date : 2020-09-02
    Michael Stephen Fiske

    Our goal is to construct mathematical operations that combine non-determinism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about operations applied to computably enumerable (c.e.) and bi-immune sets are proven here, where the objective is for the operations to preserve bi-immunity. While developing

    更新日期:2020-09-10
  • Variational wavefunctions for Sachdev-Ye-Kitaev models
    arXiv.cs.CC Pub Date : 2020-09-08
    Arijit Haldar; Omid Tavakol; Thomas Scaffidi

    Given a class of $q$-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, like for the Sachdev-Ye-Kitaev (SYK) models. This

    更新日期:2020-09-10
  • Tight List-Sizes for Oblivious AVCs under Constraints
    arXiv.cs.CC Pub Date : 2020-09-08
    Yihan Zhang; Sidharth Jaggi; Amitalok J. Budkuley

    We study list-decoding over adversarial channels governed by oblivious adversaries (a.k.a. oblivious Arbitrarily Varying Channels (AVCs)). This type of adversaries aims to maliciously corrupt the communication without knowing the actual transmission from the sender. For any oblivious AVCs potentially with constraints on the sender's transmitted sequence and the adversary's noise sequence, we determine

    更新日期:2020-09-10
  • A Fast Randomized Algorithm for Finding the Maximal Common Subsequences
    arXiv.cs.CC Pub Date : 2020-09-07
    Jin Cao; Dewei Zhong

    Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS) for $L$ strings is NP-hard, e.g., the computational complexity is exponential in $L$. In this paper, we develop a randomized algorithm, referred to as {\em Random-MCS}

    更新日期:2020-09-10
  • A Simpler NP-Hardness Proof for Familial Graph Compression
    arXiv.cs.CC Pub Date : 2020-09-07
    Ammar Ahmed; Zohair Raza Hassan; Mudassir Shabbir

    This document presents a simpler proof showcasing the NP-hardness of Familial Graph Compression.

    更新日期:2020-09-08
  • Optimal Inapproximability of Satisfiable $k$-LIN over Non-Abelian Groups
    arXiv.cs.CC Pub Date : 2020-09-06
    Amey Bhangale; Subhash Khot

    A seminal result of H\r{a}stad [J. ACM, 48(4):798--859, 2001] shows that it is NP-hard to find an assignment that satisfies $\frac{1}{|G|}+\varepsilon$ fraction of the constraints of a given $k$-LIN instance over an abelian group, even if there is an assignment that satisfies $(1-\varepsilon)$ fraction of the constraints, for any constant $\varepsilon>0$. Engebretsen et al. [Theoretical Computer Science

    更新日期:2020-09-08
  • On Hardness of Approximation of Parameterized Set Cover and Label Cover: Threshold Graphs from Error Correcting Codes
    arXiv.cs.CC Pub Date : 2020-09-06
    Karthik C. S.; Inbal Livni-Navon

    In the $(k,h)$-SetCover problem, we are given a collection $\mathcal{S}$ of sets over a universe $U$, and the goal is to distinguish between the case that $\mathcal{S}$ contains $k$ sets which cover $U$, from the case that at least $h$ sets in $\mathcal{S}$ are needed to cover $U$. Lin (ICALP'19) recently showed a gap creating reduction from the $(k,k+1)$-SetCover problem on universe of size $O_k(\log

    更新日期:2020-09-08
  • Towards Stronger Counterexamples to the Log-Approximate-Rank Conjecture
    arXiv.cs.CC Pub Date : 2020-09-06
    Arkadev Chattopadhyay; Ankit Garg; Suhail Sherif

    We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at most $O(n^3)$ and randomized parity decision tree complexity $\Theta(n)$. This improves upon the recent work of Chattopadhyay, Mande and Sherif (JACM '20) both qualitatively

    更新日期:2020-09-08
  • A Lower Bound on Determinantal Complexity
    arXiv.cs.CC Pub Date : 2020-09-05
    Mrinal Kumar; Ben Lee Volk

    The determinantal complexity of a polynomial $P \in \mathbb{F}[x_1, \ldots, x_n]$ over a field $\mathbb{F}$ is the dimension of the smallest matrix $M$ whose entries are affine functions in $\mathbb{F}[x_1, \ldots, x_n]$ such that $P = Det(M)$. We prove that the determinantal complexity of the polynomial $\sum_{i = 1}^n x_i^n$ is at least $1.5n - 3$. For every $n$-variate polynomial of degree $d$,

    更新日期:2020-09-08
  • Fast simulation of planar Clifford circuits
    arXiv.cs.CC Pub Date : 2020-09-07
    David Gosset; Daniel Grier; Alex Kerzner; Luke Schaeffer

    A general quantum circuit can be simulated in exponential time on a classical computer. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more generally exponential in the treewidth of the underlying graph. Separately, Gottesman and Knill showed that if all gates are restricted to be Clifford, then

    更新日期:2020-09-08
  • Multi-Pass Graph Streaming Lower Bounds for Cycle Counting, MAX-CUT, Matching Size, and Other Problems
    arXiv.cs.CC Pub Date : 2020-09-07
    Sepehr Assadi; Gillat Kol; Raghuvansh R. Saxena; Huacheng Yu

    Consider the following gap cycle counting problem in the streaming model: The edges of a $2$-regular $n$-vertex graph $G$ are arriving one-by-one in a stream and we are promised that $G$ is a disjoint union of either $k$-cycles or $2k$-cycles for some small $k$; the goal is to distinguish between these two cases. Verbin and Yu [SODA 2011] introduced this problem and showed that any single-pass streaming

    更新日期:2020-09-08
  • Strong rainbow disconnection in graphs
    arXiv.cs.CC Pub Date : 2020-09-06
    Xuqing Bai; Xueliang Li

    Let $G$ be a nontrivial edge-colored connected graph. An edge-cut $R$ of $G$ is called a {\it rainbow edge-cut} if no two edges of $R$ are colored with the same color. For two distinct vertices $u$ and $v$ of $G$, if an edge-cut separates them, then the edge-cut is called a {\it $u$-$v$-edge-cut}. An edge-colored graph $G$ is called \emph{strong rainbow disconnected} if for every two distinct vertices

    更新日期:2020-09-08
  • Sum-of-Squares Lower Bounds for Sherrington-Kirkpatrick via Planted Affine Planes
    arXiv.cs.CC Pub Date : 2020-09-03
    Mrinalkanti Ghosh; Fernando Granha Jeronimo; Chris Jones; Aaron Potechin; Goutham Rajendran

    The Sum-of-Squares (SoS) hierarchy is a semi-definite programming meta-algorithm that captures state-of-the-art polynomial time guarantees for many optimization problems such as Max-$k$-CSPs and Tensor PCA. On the flip side, a SoS lower bound provides evidence of hardness, which is particularly relevant to average-case problems for which NP-hardness may not be available. In this paper, we consider

    更新日期:2020-09-08
  • Circuit Satisfiability Problem for circuits of small complexity
    arXiv.cs.CC Pub Date : 2020-09-02
    Marsel Matdinov

    The following problem is considered. A Turing machine $M$, that accepts a string of fixed length $t$ as input, runs for a time not exceeding a fixed value $n$ and is guaranteed to produce a binary output, is given. It's required to find a string $X$ such that $M(X) = 1$ effectively in terms of $t$, $n$, the size of the alphabet of $M$ and the number of states of $M$. The problem is close to the well-known

    更新日期:2020-09-03
  • Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms
    arXiv.cs.CC Pub Date : 2020-09-02
    Sepehr Assadi; Ran Raz

    We prove that any two-pass graph streaming algorithm for the $s$-$t$ reachability problem in $n$-vertex directed graphs requires near-quadratic space of $n^{2-o(1)}$ bits. As a corollary, we also obtain near-quadratic space lower bounds for several other fundamental problems including maximum bipartite matching and (approximate) shortest path in undirected graphs. Our results collectively imply that

    更新日期:2020-09-03
  • On the existence of hidden machines in computational time hierarchies
    arXiv.cs.CC Pub Date : 2020-09-02
    Felipe S. Abrahão; Klaus Wehmuth; Artur Ziviani

    Challenging the standard notion of totality in computable functions, one has that, given any sufficiently expressive formal axiomatic system, there are total functions that, although computable and "intuitively" understood as being total, cannot be proved to be total. In this article we show that this implies the existence of an infinite hierarchy of time complexity classes whose representative members

    更新日期:2020-09-03
  • An algorithm for dividing quaternions
    arXiv.cs.CC Pub Date : 2020-08-30
    Aleksandr Cariow; Galina Cariowa

    In this work, a rationalized algorithm for calculating the quotient of two quaternions is presented which reduces the number of underlying real multiplications. Hardware for fast multiplication is much more expensive than hardware for fast addition. Therefore, reducing the number of multiplications in VLSI processor design is usually a desirable task. The performing of a quaternion division using the

    更新日期:2020-09-02
  • The Double Exponential Runtime is Tight for 2-Stage Stochastic ILPs
    arXiv.cs.CC Pub Date : 2020-08-29
    Klaus Jansen; Kim-Manuel Klein; Alexandra Lassota

    We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called $2$-stage stochastic. A $2$-stage stochastic ILP is an integer program of the form $\min \{w^T x \mid \mathcal{A} x = b, L \leq x \leq U, x \in \mathbb{Z}^{s + nt} \}$ where the constraint matrix $\mathcal{A} \in \mathbb{Z}^{r n \times s +nt}$ consists

    更新日期:2020-09-01
  • Is the space complexity of planted clique recovery the same as that of detection?
    arXiv.cs.CC Pub Date : 2020-08-28
    Jay Mardia

    We study the planted clique problem in which a clique of size k is planted in an Erd\H{o}s-R\'enyi graph G(n, 1/2), and one is interested in either detecting or recovering this planted clique. This problem is interesting because it is widely believed to show a statistical-computational gap at clique size k=sqrt{n}, and has emerged as the prototypical problem with such a gap from which average-case

    更新日期:2020-09-01
  • Edmonds' problem and the membership problem for orbit semigroups of quiver representations
    arXiv.cs.CC Pub Date : 2020-08-31
    Calin Chindris; Daniel Kline

    A central problem in algebraic complexity, posed by J. Edmonds, asks to decide if the span of a given $l$-tuple $\V=(\V_1, \ldots, \V_l)$ of $N \times N$ complex matrices contains a non-singular matrix. In this paper, we provide a quiver invariant theoretic approach to this problem. Viewing $\V$ as a representation of the $l$-Kronecker quiver $\K_l$, Edmonds' problem can be rephrased as asking to decide

    更新日期:2020-09-01
  • Semipaired Domination in Some Subclasses of Chordal Graphs
    arXiv.cs.CC Pub Date : 2020-08-31
    Michael A. Henning; Arti Pandey; Vikash Tripathi

    A dominating set $D$ of a graph $G$ without isolated vertices is called semipaired dominating set if $D$ can be partitioned into $2$-element subsets such that the vertices in each set are at distance at most $2$. The semipaired domination number, denoted by $\gamma_{pr2}(G)$ is the minimum cardinality of a semipaired dominating set of $G$. Given a graph $G$ with no isolated vertices, the \textsc{Minimum

    更新日期:2020-09-01
  • Recoverable Robust Representatives Selection Problems with Discrete Budgeted Uncertainty
    arXiv.cs.CC Pub Date : 2020-08-28
    Marc Goerigk; Stefan Lendl; Lasse Wulf

    Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose a fixed number of items from several disjoint sets, such that the worst-case costs after taking a recovery action are as small as possible. The uncertainty is modeled

    更新日期:2020-08-31
  • Spectral Planting and the Hardness of Refuting Cuts, Colorability, and Communities in Random Graphs
    arXiv.cs.CC Pub Date : 2020-08-27
    Afonso S. Bandeira; Jess Banks; Dmitriy Kunisky; Cristopher Moore; Alexander S. Wein

    We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-case computational hardness for this problem in sparse random regular graphs, showing optimality of a simple spectral certificate. This evidence takes the form of a computationally-quiet planting: we construct a distribution

    更新日期:2020-08-28
  • Simple Reductions from Formula-SAT to Pattern Matching on Labeled Graphs and Subtree Isomorphism
    arXiv.cs.CC Pub Date : 2020-08-26
    Daniel Gibney; Gary Hoppenworth; Sharma V. Thankachan

    The CNF formula satisfiability problem (CNF-SAT) has been reduced to many fundamental problems in P to prove tight lower bounds under the Strong Exponential Time Hypothesis (SETH). Recently, the works of Abboud, Hansen, Vassilevska W. and Williams (STOC 16), and later, Abboud and Bringmann (ICALP 18) have proposed basing lower bounds on the hardness of general boolean formula satisfiability (Formula-SAT)

    更新日期:2020-08-28
  • Complexity Aspects of Fundamental Questions in Polynomial Optimization
    arXiv.cs.CC Pub Date : 2020-08-27
    Jeffrey Zhang

    In this thesis, we settle the computational complexity of some fundamental questions in polynomial optimization. These include the questions of (i) finding a local minimum, (ii) testing local minimality of a point, and (iii) deciding attainment of the optimal value. Our results characterize the complexity of these three questions for all degrees of the defining polynomials left open by prior literature

    更新日期:2020-08-28
  • Network satisfaction for symmetric relation algebras with a flexible atom
    arXiv.cs.CC Pub Date : 2020-08-27
    Manuel Bodirsky; Simon Knäuer

    Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify the computational complexity of the network satisfaction problem for all finite relation algebras $\bf A$. We provide a complete classification for the case that $\bf A$ is symmetric and has a flexible atom; the problem is in this case NP-complete or in P. If a finite integral relation algebra has a flexible atom, then it has a

    更新日期:2020-08-28
  • Inapproximability of Diameter in super-linear time: Beyond the 5/3 ratio
    arXiv.cs.CC Pub Date : 2020-08-26
    Édouard Bonnet

    We show, assuming the Strong Exponential Time Hypothesis, that for every $\varepsilon > 0$, approximating directed Diameter on $m$-arc graphs within ratio $7/4 - \varepsilon$ requires $m^{4/3 - o(1)}$ time. Our construction uses nonnegative edge weights but even holds for sparse digraphs, i.e., for which the number of vertices $n$ and the number of arcs $m$ satisfy $m = n \log^{O(1)} n$. This is the

    更新日期:2020-08-27
  • An Optimal Separation of Randomized and Quantum Query Complexity
    arXiv.cs.CC Pub Date : 2020-08-24
    Alexander A. Sherstov; Andrey A. Storozhenko; Pei Wu

    We prove that for every decision tree, the absolute values of the Fourier coefficients of given order $\ell\geq1$ sum to at most $c^{\ell}\sqrt{\binom{d}{\ell}(1+\log n)^{\ell-1}},$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant. This bound is essentially tight and settles a conjecture due to Tal (arxiv 2019; FOCS 2020). The bounds prior to our work degraded

    更新日期:2020-08-25
  • Digraphs Homomorphism Problems with Maltsev Condition
    arXiv.cs.CC Pub Date : 2020-08-22
    Jeff Kinne; Ashwin Murali; Arash Rafiey

    We consider a generalization of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$, HOM($H$). In this setting, we are given an input digraph $G$ together with a list function from $G$ to $2^H$. The goal is to find a homomorphism from $G$ to $H$ with respect to the lists if one exists. We show that if the list function is a Maltsev polymorphism then deciding whether $G$ admits a

    更新日期:2020-08-25
  • Deletion to Induced Matching
    arXiv.cs.CC Pub Date : 2020-08-21
    Akash Kumar; Mithilesh Kumar

    In the DELETION TO INDUCED MATCHING problem, we are given a graph $G$ on $n$ vertices, $m$ edges and a non-negative integer $k$ and asks whether there exists a set of vertices $S \subseteq V(G) $ such that $|S|\le k$ and the size of any connected component in $G-S$ is exactly 2. In this paper, we provide a fixed-parameter tractable (FPT) algorithm of running time $O^*(1.748^{k})$ for the DELETION TO

    更新日期:2020-08-25
  • Indistinguishability Obfuscation from Well-Founded Assumptions
    arXiv.cs.CC Pub Date : 2020-08-21
    Aayush Jain; Huijia Lin; Amit Sahai

    In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: Let $\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)$ be arbitrary constants. Assume sub-exponential security of the following assumptions, where $\lambda$ is a security parameter, and the parameters $\ell,k,n$ below are large enough polynomials

    更新日期:2020-08-24
  • On Fine-Grained Exact Computation in Regular Graphs
    arXiv.cs.CC Pub Date : 2020-08-20
    Saeed Akhoondian Amiri

    We show that there is no subexponential time algorithm for computing the exact solution of the maximum independent set problem in $d$-regular graphs, for any constant $d>2$, unless ETH fails. We also discuss the extensions of our construction to other problems and other classes of graphs, including $5$-regular planar graphs.

    更新日期:2020-08-21
  • A Direct Product Theorem for One-Way Quantum Communication
    arXiv.cs.CC Pub Date : 2020-08-20
    Rahul Jain; Srijita Kundu

    We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, \zeta > 0$ and any $k\geq1$, we show that \[ \mathrm{Q}^1_{1-(1-\varepsilon)^{\Omega(\zeta^6k/\log|\mathcal{Z}|)}}(f^k) = \Omega\left(k\left(\zeta^5\cdot\mathrm{Q}^1_{\varepsilon + 12\zeta}(f)

    更新日期:2020-08-21
  • The Quantum Supremacy Tsirelson Inequality
    arXiv.cs.CC Pub Date : 2020-08-20
    William Kretschmer

    A leading proposal for verifying near-term quantum supremacy experiments on noisy random quantum circuits is linear cross-entropy benchmarking. For a quantum circuit $C$ on $n$ qubits and a sample $z \in \{0,1\}^n$, the benchmark involves computing $|\langle z|C|0^n \rangle|^2$, i.e. the probability of measuring $z$ from the output distribution of $C$ on the all zeros input. Under a strong conjecture

    更新日期:2020-08-21
  • Solving problems on generalized convex graphs via mim-width
    arXiv.cs.CC Pub Date : 2020-08-20
    Nick Brettell; Andrea Munaro; Daniël Paulusma

    A bipartite graph $G=(A,B,E)$ is ${\cal H}$-convex, for some family of graphs ${\cal H}$, if there exists a graph $H\in {\cal H}$ with $V(H)=A$ such that the set of neighbours in $A$ of each $b\in B$ induces a connected subgraph of $H$. A variety of well-known $\mathsf{NP}$-complete problems, including \textsc{Dominating Set}, \textsc{Feedback Vertex Set}, \textsc{Induced Matching} and \textsc{List

    更新日期:2020-08-21
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