当前期刊: arXiv - CS - Computational Complexity Go to current issue    加入关注   
显示样式:        排序: IF: - GO 导出
我的关注
我的收藏
您暂时未登录!
登录
  • Quantum algorithms for matrix scaling and matrix balancing
    arXiv.cs.CC Pub Date : 2020-11-25
    Joran van Apeldoorn; Sander Gribling; Yinan Li; Harold Nieuwboer; Michael Walter; Ronald de Wolf

    Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the power and limitations of quantum algorithms for these problems. We provide quantum implementations of two classical (in both senses of the word) methods: Sinkhorn's

    更新日期:2020-11-27
  • Mixed-Integer Linear Programming Models for Multi-Robot Non-Adversarial Search
    arXiv.cs.CC Pub Date : 2020-11-25
    Beatriz A. Asfora; Jacopo Banfi; Mark Campbell

    In this letter, we consider the Multi-Robot Efficient Search Path Planning (MESPP) problem, where a team of robots is deployed in a graph-represented environment to capture a moving target within a given deadline. We prove this problem to be NP-hard, and present the first set of Mixed-Integer Linear Programming (MILP) models to tackle the MESPP problem. Our models are the first to encompass multiple

    更新日期:2020-11-27
  • Arithmetic Expression Construction
    arXiv.cs.CC Pub Date : 2020-11-23
    Leo Alcock; Sualeh Asif; Jeffrey Bosboom; Josh Brunner; Charlotte Chen; Erik D. Demaine; Rogers Epstein; Adam Hesterberg; Lior Hirschfeld; William Hu; Jayson Lynch; Sarah Scheffler; Lillian Zhang

    When can $n$ given numbers be combined using arithmetic operators from a given subset of $\{+, -, \times, \div\}$ to obtain a given target number? We study three variations of this problem of Arithmetic Expression Construction: when the expression (1) is unconstrained; (2) has a specified pattern of parentheses and operators (and only the numbers need to be assigned to blanks); or (3) must match a

    更新日期:2020-11-25
  • Recognizing Proper Tree-Graphs
    arXiv.cs.CC Pub Date : 2020-11-23
    Steven Chaplick; Petr A. Golovach; Tim A. Hartmann; Dušan Knop

    We investigate the parameterized complexity of the recognition problem for the proper $H$-graphs. The $H$-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph $H$, and the properness means that the containment relationship between the representations of the vertices is forbidden. The class of $H$-graphs was introduced as a natural (parameterized) generalization

    更新日期:2020-11-25
  • InstaHide's Sample Complexity When Mixing Two Private Images
    arXiv.cs.CC Pub Date : 2020-11-24
    Baihe Huang; Zhao Song; Runzhou Tao; Ruizhe Zhang; Danyang Zhuo

    Inspired by InstaHide challenge [Huang, Song, Li and Arora'20], [Chen, Song and Zhuo'20] recently provides one mathematical formulation of InstaHide attack problem under Gaussian images distribution. They show that it suffices to use $O(n_{\mathsf{priv}}^{k_{\mathsf{priv}} - 2/(k_{\mathsf{priv}} + 1)})$ samples to recover one private image in $n_{\mathsf{priv}}^{O(k_{\mathsf{priv}})} + \mathrm{pol

    更新日期:2020-11-25
  • On algorithms to find p-ordering
    arXiv.cs.CC Pub Date : 2020-11-22
    Aditya Gulati; Sayak Chakrabarti; Rajat Mittal

    The concept of p-ordering for a prime p was introduced by Manjul Bhargava (in his PhD thesis) to develop a generalized factorial function over an arbitrary subset of integers. This notion of p-ordering provides a representation of polynomials modulo prime powers, and has been used to prove properties of roots sets modulo prime powers. We focus on the complexity of finding a p-ordering given a prime

    更新日期:2020-11-25
  • Analysis of Movement-Based Connectivity Restoration Problem in Wireless Ad-Hoc and Sensor Networks
    arXiv.cs.CC Pub Date : 2020-11-21
    Umut Can Cabuk; Vahid Khalilpour Akram; Orhan Dagdeviren

    Topology control, including topology construction and maintenance phases, is a vital conception for wireless ad-hoc networks of any kind, expressly the wireless sensor networks (WSN). Topology maintenance, the latter phase, concerns several problems, such as optimizing the energy consumption, increasing the data rate, making clusters, and sustaining the connectivity. A disconnected network, among other

    更新日期:2020-11-25
  • Near-Optimal Data Source Selection for Bayesian Learning
    arXiv.cs.CC Pub Date : 2020-11-21
    Lintao Ye; Aritra Mitra; Shreyas Sundaram

    We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First, we show that the data source selection problem for Bayesian learning is NP-hard. We then show that the data source selection problem can be transformed into an instance

    更新日期:2020-11-25
  • Space Lower Bounds for Graph Stream Problems
    arXiv.cs.CC Pub Date : 2020-11-20
    Paritosh Verma

    This work concerns with proving space lower bounds for graph problems in the streaming model. It is known that computing the length of shortest path between two nodes in the streaming model requires $\Omega(n)$ space, where $n$ is the number of nodes in the graph. We study the problem of finding the depth of a given node in a rooted tree in the streaming model. For this problem we prove a tight single

    更新日期:2020-11-23
  • On the directed tile assembly systems at temperature 1
    arXiv.cs.CC Pub Date : 2020-11-18
    Pierre-Étienne Meunier; Damien Regnault

    We show here that a model called directed self-assembly at temperature 1 is unable to do complex computations like the ones of a Turing machine. Since this model can be seen as a generalization of finite automata to 2D languages, a logical approach is to proceed in two steps. The first one is to develop a 2D pumping lemma and the second one is to use this pumping lemma to classify the different types

    更新日期:2020-11-21
  • Hyperpaths
    arXiv.cs.CC Pub Date : 2020-11-19
    Amir Dahari; Nati Linial

    Hypertrees are high-dimensional counterparts of graph theoretic trees. They have attracted a great deal of attention by various investigators. Here we introduce and study Hyperpaths -- a particular class of hypertrees which are high dimensional analogs of paths in graph theory. A $d$-dimensional hyperpath is a $d$-dimensional hypertree in which every $(d-1)$-dimensional face is contained in at most

    更新日期:2020-11-21
  • Cluster structure of optimal solutions in bipartitioning of small worlds
    arXiv.cs.CC Pub Date : 2020-11-19
    Adam Lipowski; Antonio L. Ferreira; Dorota Lipowska

    Using a simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behaviour, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show

    更新日期:2020-11-21
  • (Sub)Exponential advantage of adiabatic quantum computation with no sign problem
    arXiv.cs.CC Pub Date : 2020-11-18
    András Gilyén; Umesh Vazirani

    We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by Hastings. The Hamiltonian that exhibits this speed-up comes from the adjacency matrix of an undirected graph, and we can view the adiabatic evolution as an efficient

    更新日期:2020-11-21
  • Dichotomy Result on 3-Regular Bipartite Non-negative Functions
    arXiv.cs.CC Pub Date : 2020-11-18
    Austen Z. Fan; Jin-Yi Cai

    We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function $f = [x_0, x_1, x_2, x_3]$, we prove that the bipartite Holant problem $\operatorname{Holant} \left( f \mid \left( =_3 \right) \right)$ is \emph{either} computable in polynomial time \emph{or} $\#$P-hard. The dichotomy criterion

    更新日期:2020-11-19
  • Proof Compression and NP Versus PSPACE II: Addendum
    arXiv.cs.CC Pub Date : 2020-11-17
    L. Gordeev; E. H. Hermann

    In [3] we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier's cut-free sequent calculus for minimal logic (HSC) [5] with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction (ND) [6]. In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea (due to the second author)

    更新日期:2020-11-19
  • Block Rigidity: Strong Multiplayer Parallel Repetition implies Super-Linear Lower Bounds for Turing Machines
    arXiv.cs.CC Pub Date : 2020-11-18
    Kunal Mittal; Ran Raz

    We prove that a sufficiently strong parallel repetition theorem for a special case of multiplayer (multiprover) games implies super-linear lower bounds for multi-tape Turing machines with advice. To the best of our knowledge, this is the first connection between parallel repetition and lower bounds for time complexity and the first major potential implication of a parallel repetition theorem with more

    更新日期:2020-11-19
  • Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing
    arXiv.cs.CC Pub Date : 2020-11-18
    Hadley Black; Iden Kalemaj; Sofya Raskhodnikova

    We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra~(SICOMP 2018) for Boolean functions to the case of real-valued functions $f \colon \{0,1\}^d\to\mathbb{R}$. Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real-valued function $f$ over an arbitrary partially ordered domain as a collection of Boolean functions

    更新日期:2020-11-19
  • Exact nuclear norm, completion and decomposition for random overcomplete tensors via degree-4 SOS
    arXiv.cs.CC Pub Date : 2020-11-18
    Bohdan Kivva; Aaron Potechin

    In this paper we show that simple semidefinite programs inspired by degree $4$ SOS can exactly solve the tensor nuclear norm, tensor decomposition, and tensor completion problems on tensors with random asymmetric components. More precisely, for tensor nuclear norm and tensor decomposition, we show that w.h.p. these semidefinite programs can exactly find the nuclear norm and components of an $(n\times

    更新日期:2020-11-19
  • Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings
    arXiv.cs.CC Pub Date : 2020-11-16
    Joel Rajakumar; Jai Moondra; Swati Gupta; Creston D. Herold

    We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware to find approximate solutions to Max-Cut. We present a mathematical description of the problem and provide approximately optimal algorithmic constructions

    更新日期:2020-11-17
  • The Longest Run Subsequence Problem: Further Complexity Results
    arXiv.cs.CC Pub Date : 2020-11-16
    Riccardo Dondi; Florian Sikora

    Longest Run Subsequence is a problem introduced recently in the context of the scaffolding phase of genome assembly (Schrinner et al.,WABI 2020). The problem asks for a maximum length subsequence of a given string that contains at most one run for each symbol (a run is a maximum substring of consecutive identical symbols). The problem has been shown to be NP-hard and to be fixed-parameter tractable

    更新日期:2020-11-17
  • Polynomial-time Tests for Difference Terms in Idempotent Varieties
    arXiv.cs.CC Pub Date : 2020-11-16
    William DeMeo; Ralph Freese; Matthew Valeriote

    We consider the following practical question: given a finite algebra A in a finite language, can we efficiently decide whether the variety generated by A has a difference term? We answer this question (positively) in the idempotent case and then describe algorithms for constructing difference term operations.

    更新日期:2020-11-17
  • Conjugacy of reversible cellular automata
    arXiv.cs.CC Pub Date : 2020-11-16
    Ville Salo

    We show that conjugacy of reversible cellular automata is undecidable, whether the conjugacy is to be performed by another reversible cellular automaton or by a general homeomorphism. This gives rise to a new family of f.g. groups with undecidable conjugacy problems, whose descriptions arguably do not involve any type of computation. For many automorphism groups of subshifts, as well as the group of

    更新日期:2020-11-17
  • Acceleration of stochastic methods on the example of decentralized SGD
    arXiv.cs.CC Pub Date : 2020-11-15
    Trimbach Ekaterina; Rogozin Alexander

    In this paper, we present an algorithm for accelerating decentralized stochastic gradient descent. Recently, decentralized stochastic optimization methods have attracted a lot of attention, mainly due to their low iteration cost, data locality and data exchange efficiency. They are generalizations of algorithms such as SGD and Local SGD. An additional important contribution of this work is the additions

    更新日期:2020-11-17
  • Separating the Communication Complexity of Truthful and Non-Truthful Combinatorial Auctions
    arXiv.cs.CC Pub Date : 2020-11-14
    Sepehr Assadi; Hrishikesh Khandeparkar; Raghuvansh R. Saxena; S. Matthew Weinberg

    We provide the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-approximation for two buyers with XOS valuations over $m$ items requires $\exp(\Omega(\varepsilon^2 \cdot m))$ communication, whereas a

    更新日期:2020-11-17
  • Reconfiguration of Connected Graph Partitions via Recombination
    arXiv.cs.CC Pub Date : 2020-11-14
    Hugo A. Akitaya; Matias Korman; Oliver Korten; Diane L. Souvaine; Csaba D. Tóth

    Motivated by applications in gerrymandering detection, we study a reconfiguration problem on connected partitions of a connected graph $G$. A partition of $V(G)$ is \emph{connected} if every part induces a connected subgraph. In many applications, it is desirable to obtain parts of roughly the same size, possibly with some slack $s$. A \emph{Balanced Connected $k$-Partition with slack $s$}, denoted

    更新日期:2020-11-17
  • Communication complexity of Nash equilibrium in potential games
    arXiv.cs.CC Pub Date : 2020-11-12
    Yakov Babichenko; Aviad Rubinstein

    We prove communication complexity lower bounds for (possibly mixed) Nash equilibrium in potential games. In particular, we show that finding a Nash equilibrium requires $poly(N)$ communication in two-player $N \times N$ potential games, and $2^{poly(n)}$ communication in $n$-player two-action games. To the best of our knowledge, these are the first results to demonstrate hardness in any model of (possibly

    更新日期:2020-11-16
  • Comparing computational entropies below majority (or: When is the dense model theorem false?)
    arXiv.cs.CC Pub Date : 2020-11-12
    Russell Impagliazzo; Sam McGuire

    Computational pseudorandomness studies the extent to which a random variable $\bf{Z}$ looks like the uniform distribution according to a class of tests $\cal{F}$. Computational entropy generalizes computational pseudorandomness by studying the extent which a random variable looks like a \emph{high entropy} distribution. There are different formal definitions of computational entropy with different

    更新日期:2020-11-13
  • Total Completion Time Minimization for Scheduling with Incompatibility Cliques
    arXiv.cs.CC Pub Date : 2020-11-12
    Klaus Jansen; Alexandra Lassota; Marten Maack; Tytus Pikies

    This paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph and no two jobs connected by an edge are allowed to be assigned to the same machine. In particular, we study the case where the graph is a collection of disjoint cliques. Scheduling with incompatibilities between jobs represents a well-established line of research in scheduling theory and the

    更新日期:2020-11-13
  • Hardness of Approximate Nearest Neighbor Search under L-infinity
    arXiv.cs.CC Pub Date : 2020-11-12
    Young Kun Ko; Min Jae Song

    We show conditional hardness of Approximate Nearest Neighbor Search (ANN) under the $\ell_\infty$ norm with two simple reductions. Our first reduction shows that hardness of a special case of the Shortest Vector Problem (SVP), which captures many provably hard instances of SVP, implies a lower bound for ANN with polynomial preprocessing time under the same norm. Combined with a recent quantitative

    更新日期:2020-11-13
  • Efficient Solution of Boolean Satisfiability Problems with Digital MemComputing
    arXiv.cs.CC Pub Date : 2020-11-12
    S. R. B. Bearden; Y. R. Pei; M. Di Ventra

    Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution methods in a variety of applications. It is the decision problem of determining whether a Boolean formula has a satisfying assignment, believed to require exponentially

    更新日期:2020-11-13
  • Quantum Random Access Codes for Boolean Functions
    arXiv.cs.CC Pub Date : 2020-11-12
    João F. Doriguello; Ashley Montanaro

    An $n\overset{p}{\mapsto}m$ random access code (RAC) is an encoding of $n$ bits into $m$ bits such that any initial bit can be recovered with probability at least $p$, while in a quantum RAC (QRAC), the $n$ bits are encoded into $m$ qubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access

    更新日期:2020-11-13
  • Efficient List-Decoding with Constant Alphabet and List Sizes
    arXiv.cs.CC Pub Date : 2020-11-11
    Zeyu Guo; Noga Ron-Zewi

    We present an explicit and efficient algebraic construction of capacity-achieving list decodable codes with both constant alphabet and constant list sizes. More specifically, for any $R \in (0,1)$ and $\epsilon>0$, we give an algebraic construction of an infinite family of error-correcting codes of rate $R$, over an alphabet of size $(1/\epsilon)^{O(1/\epsilon^2)}$, that can be list decoded from a

    更新日期:2020-11-12
  • Ordinally Consensus Subset over Multiple Metrics
    arXiv.cs.CC Pub Date : 2020-11-11
    Dingkang Wang; Yusu Wang

    In this paper, we propose to study the following maximum ordinal consensus problem: Suppose we are given a metric system (M, X), which contains k metrics M = {\rho_1,..., \rho_k} defined on the same point set X. We aim to find a maximum subset X' of X such that all metrics in M are "consistent" when restricted on the subset X'. In particular, our definition of consistency will rely only on the ordering

    更新日期:2020-11-12
  • The Strongish Planted Clique Hypothesis and Its Consequences
    arXiv.cs.CC Pub Date : 2020-11-11
    Pasin Manurangsi; Aviad Rubinstein; Tselil Schramm

    We formulate a new hardness assumption, the Strongish Planted Clique Hypothesis (SPCH), which postulates that any algorithm for planted clique must run in time $n^{\Omega(\log{n})}$ (so that the state-of-the-art running time of $n^{O(\log n)}$ is optimal up to a constant in the exponent). We provide two sets of applications of the new hypothesis. First, we show that SPCH implies (nearly) tight inapproximability

    更新日期:2020-11-12
  • StoqMA meets distribution testing
    arXiv.cs.CC Pub Date : 2020-11-11
    Yupan Liu

    $\mathsf{StoqMA}$ captures the computational hardness of approximating the ground energy of local Hamiltonians that do not suffer the so-called sign problem. We provide a novel connection between $\mathsf{StoqMA}$ and the distribution testing via reversible circuits. First, we prove that easy-witness $\mathsf{StoqMA}$ (viz. $\mathsf{eStoqMA}$, a sub-class of $\mathsf{StoqMA}$) is contained in $\mathsf{MA}$

    更新日期:2020-11-12
  • Three Candidate Plurality is Stablest for Small Correlations
    arXiv.cs.CC Pub Date : 2020-11-11
    Steven Heilman; Alex Tarter

    Using the calculus of variations, we prove the following structure theorem for noise stable partitions: a partition of $n$-dimensional Euclidean space into $m$ disjoint sets of fixed Gaussian volumes that maximize their noise stability must be $(m-1)$-dimensional, if $m-1\leq n$. In particular, the maximum noise stability of a partition of $m$ sets in $\mathbb{R}^{n}$ of fixed Gaussian volumes is constant

    更新日期:2020-11-12
  • Complexity of branch-and-bound and cutting planes in mixed-integer optimization -- II
    arXiv.cs.CC Pub Date : 2020-11-11
    Amitabh Basu; Michele Conforti; Marco Di Summa; Hongyi Jiang

    We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut framework can be orders of magnitude more efficient than employing these tools on their own. In particular, we give general conditions under which a cutting plane

    更新日期:2020-11-12
  • On the cut dimension of a graph
    arXiv.cs.CC Pub Date : 2020-11-10
    Troy Lee; Tongyang Li; Miklos Santha; Shengyu Zhang

    Let $G = (V,w)$ be a weighted undirected graph with $m$ edges. The cut dimension of $G$ is the dimension of the span of the characteristic vectors of the minimum cuts of $G$, viewed as vectors in $\{0,1\}^m$. For every $n \ge 2$ we show that the cut dimension of an $n$-vertex graph is at most $2n-3$, and construct graphs realizing this bound. The cut dimension was recently defined by Graur et al.\

    更新日期:2020-11-12
  • On Counting (Quantum-)Graph Homomorphisms in Finite Fields
    arXiv.cs.CC Pub Date : 2020-11-09
    J. A. Gregor Lagodzinski; Andreas Göbel; Katrin Casel; Tobias Friedrich

    We study the problem of counting the number of homomorphisms from an input graph $G$ to a fixed (quantum) graph $\bar{H}$ in any finite field of prime order $\mathbb{Z}_p$. The subproblem with graph $H$ was introduced by Faben and Jerrum~[ToC'15] and its complexity is still uncharacterised despite active research, e.g. the very recent work of Focke, Goldberg, Roth, and Zivn\'y~[SODA'21]. Our contribution

    更新日期:2020-11-12
  • Graph Homomorphism Polynomials: Algorithms and Complexity
    arXiv.cs.CC Pub Date : 2020-11-09
    Balagopal Komarath; Anurag Pandey; C. S. Rahul

    We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new algorithms for counting and detecting graph patterns, and also for obtaining natural polynomial families which are complete for algebraic complexity classes $\mathsf{VBP}$

    更新日期:2020-11-12
  • High Dimensional Expanders: Random Walks, Pseudorandomness, and Unique Games
    arXiv.cs.CC Pub Date : 2020-11-09
    Max Hopkins; Tali Kaufman; Shachar Lovett

    Higher order random walks (HD-walks) on high dimensional expanders have played a crucial role in a number of recent breakthroughs in theoretical computer science, perhaps most famously in the recent resolution of the Mihail-Vazirani conjecture (Anari et al. STOC 2019), which focuses on HD-walks on one-sided local-spectral expanders. In this work we study the spectral structure of walks on the stronger

    更新日期:2020-11-12
  • Machinery for Proving Sum-of-Squares Lower Bounds on Certification Problems
    arXiv.cs.CC Pub Date : 2020-11-09
    Aaron Potechin; Goutham Rajendran

    In this paper, we construct general machinery for proving Sum-of-Squares lower bounds on certification problems by generalizing the techniques used by Barak et al. [FOCS 2016] to prove Sum-of-Squares lower bounds for planted clique. Using this machinery, we prove degree $n^{\epsilon}$ Sum-of-Squares lower bounds for tensor PCA, the Wishart model of sparse PCA, and a variant of planted clique which

    更新日期:2020-11-12
  • Hardness of Approximation of Euclidean $k$-Median
    arXiv.cs.CC Pub Date : 2020-11-09
    Anup Bhattacharya; Dishant Goyal; Ragesh Jaiswal

    The Euclidean $k$-median problem is defined in the following manner: given a set $\mathcal{X}$ of $n$ points in $\mathbb{R}^{d}$, and an integer $k$, find a set $C \subset \mathbb{R}^{d}$ of $k$ points (called centers) such that the cost function $\Phi(C,\mathcal{X}) \equiv \sum_{x \in \mathcal{X}} \min_{c \in C} \|x-c\|_{2}$ is minimized. The Euclidean $k$-means problem is defined similarly by replacing

    更新日期:2020-11-12
  • Optimal tiling of the Euclidean space using symmetric bodies
    arXiv.cs.CC Pub Date : 2020-11-08
    Mark Braverman; Dor Minzer

    What is the least surface area of a symmetric body $B$ whose $\mathbb{Z}^n$ translations tile $\mathbb{R}^n$? Since any such body must have volume $1$, the isoperimetric inequality implies that its surface area must be at least $\Omega(\sqrt{n})$. Remarkably, Kindler et al.\ showed that for general bodies $B$ this is tight, i.e.\ that there is a tiling body of $\mathbb{R}^n$ whose surface area is $O(\sqrt{n})$

    更新日期:2020-11-12
  • Quantum Combinatorial Games: Structures and Computational Complexity
    arXiv.cs.CC Pub Date : 2020-11-07
    Kyle Burke; Matthew Ferland; Shang-Hua Teng

    Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in complexity, dazzling for visualization, and sophisticated for strategic reasoning-has drawn us to play concrete games full of subtleties and to characterize abstract

    更新日期:2020-11-12
  • Interactive Oracle Proofs of Proximity to Algebraic Geometry Codes
    arXiv.cs.CC Pub Date : 2020-11-09
    Sarah Bordage; Jade Nardi

    In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code $C = C(\mathcal{C}, \mathcal{P}, D)$ is a vector space associated to evaluations on $\mathcal{P}$ of functions in the Riemann-Roch space $L_{\mathcal{C}}(D)$. The problem of testing proximity to an error-correcting code $C$ consists in distinguishing between the case where an input word, given as an

    更新日期:2020-11-12
  • On the Complexity of CSP-based Ideal Membership Problems
    arXiv.cs.CC Pub Date : 2020-11-07
    Andrei A. Bulatov; Akbar Rafiey

    In this paper we consider the Ideal Membership Problem (IMP for short), in which we are given real polynomials $f_0, f_1, \dots, f_k$ and the question is to decide whether $f_0$ belongs to the ideal generated by $f_1, \dots, f_k$. In the more stringent version the task is also to find a proof of this fact. The IMP underlies many proof systems based on polynomials such as Nullstellensatz, Polynomial

    更新日期:2020-11-12
  • Smooth approximations and CSPs over finitely bounded homogeneous structures
    arXiv.cs.CC Pub Date : 2020-11-08
    Antoine Mottet; Michael Pinsker

    We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the order of the rationals. Apart from obtaining these dichotomy results, we show how our new proof technique allows to unify and significantly simplify the previous

    更新日期:2020-11-12
  • A Gap-ETH-Tight Approximation Scheme for Euclidean TSP
    arXiv.cs.CC Pub Date : 2020-11-07
    Sándor Kisfaludi-Bak; Jesper Nederlof; Karol Węgrzycki

    We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \geq 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that computes a $(1+\varepsilon)$-approximate tour, under a plausible assumption. Specifically, we give an algorithm that runs in $2^{\mathcal{O}(1/\varepsilon^{d-1})} n\log

    更新日期:2020-11-12
  • Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders
    arXiv.cs.CC Pub Date : 2020-11-06
    Marc Roth; Johannes Schmitt; Philip Wellnitz

    Given a graph property $\Phi$, we consider the problem $\mathtt{EdgeSub}(\Phi)$, where the input is a pair of a graph $G$ and a positive integer $k$, and the task is to decide whether $G$ contains a $k$-edge subgraph that satisfies $\Phi$. Specifically, we study the parameterized complexity of $\mathtt{EdgeSub}(\Phi)$ and of its counting problem $\#\mathtt{EdgeSub}(\Phi)$ with respect to both approximate

    更新日期:2020-11-09
  • Group isomorphism is nearly-linear time for most orders
    arXiv.cs.CC Pub Date : 2020-11-05
    Heiko Dietrich; James B. Wilson

    We show that there is a dense set $\Upsilon\subseteq \mathbb{N}$ of group orders and a constant $c$ such that for every $n\in \Upsilon$ we can decide in time $O(n^2(\log n)^c)$ whether two $n\times n$ multiplication tables describe isomorphic groups of order $n$. This improves significantly over the general $n^{O(\log n)}$-time complexity and shows that group isomorphism can be tested efficiently for

    更新日期:2020-11-09
  • Quantum randomized encoding, verification of quantum computing, no-cloning, and blind quantum computing
    arXiv.cs.CC Pub Date : 2020-11-05
    Tomoyuki Morimae

    Randomized encoding is a powerful cryptographic primitive with various applications such as secure multiparty computation, verifiable computation, parallel cryptography, and complexity lower-bounds. Intuitively, randomized encoding $\hat{f}$ of a function $f$ is another function such that $f(x)$ can be recovered from $\hat{f}(x)$, and nothing except for $f(x)$ is leaked from $\hat{f}(x)$. Its quantum

    更新日期:2020-11-09
  • Postulate-based proof of the P != NP hypothesis
    arXiv.cs.CC Pub Date : 2020-11-04
    O. V. German

    The paper contains a proof for the P != NP hypothesis with the help of the two "natural" postulates. The postulates restrict capacity of the Turing machines and state that each independent and necessary condition of the problem should be considered by a solver (Turing machine) individually, not in groups. That is, a solver should spend at least one step to deal with the condition and, therefore, if

    更新日期:2020-11-06
  • Consequences of APSP, triangle detection, and 3SUM hardness for separation between determinism and non-determinism
    arXiv.cs.CC Pub Date : 2020-11-04
    Andrzej Lingas

    We present implications from the known conjectures like APSP, 3SUM and ETH in a form of a negated containment of a linear-time with a non-deterministic logarithmic-bit oracle in a respective deterministic bounded-time class They are different for different conjectures and they exhibit in particular the dependency on the input range parameters. On the other hand, for the problem of verifying if an $N\times

    更新日期:2020-11-05
  • A Multistage View on 2-Satisfiability
    arXiv.cs.CC Pub Date : 2020-11-04
    Till Fluschnik

    We study $q$-SAT in the multistage model, focusing on the linear-time solvable 2-SAT. Herein, given a sequence of $q$-CNF fomulas and a non-negative integer $d$, the question is whether there is a sequence of satisfying truth assignments such that for every two consecutive truth assignments, the number of variables whose values changed is at most $d$. We prove that Multistage 2-SAT is NP-hard even

    更新日期:2020-11-05
  • PCP Theorems, SETH and More: Towards Proving Sub-linear Time Inapproximability
    arXiv.cs.CC Pub Date : 2020-11-04
    Hengzhao Ma; Jianzhong Li

    In this paper we propose the PCP-like theorem for sub-linear time inapproximability. Abboud et. have devised the distributed PCP framework for sub-quadratic time inapproximability. We show that the distributed PCP theorem can be generalized for proving arbitrary polynomial time inapproximability, but fails in the linear case. We borrow similar proof techniques from \cite{Abboud2017} for proving the

    更新日期:2020-11-05
  • Algorithms and Hardness for Linear Algebra on Geometric Graphs
    arXiv.cs.CC Pub Date : 2020-11-04
    Josh Alman; Timothy Chu; Aaron Schild; Zhao Song

    For a function $\mathsf{K} : \mathbb{R}^{d} \times \mathbb{R}^{d} \to \mathbb{R}_{\geq 0}$, and a set $P = \{ x_1, \ldots, x_n\} \subset \mathbb{R}^d$ of $n$ points, the $\mathsf{K}$ graph $G_P$ of $P$ is the complete graph on $n$ nodes where the weight between nodes $i$ and $j$ is given by $\mathsf{K}(x_i, x_j)$. In this paper, we initiate the study of when efficient spectral graph theory is possible

    更新日期:2020-11-05
  • Circuit lower bounds for quantum code Hamiltonians and an almost linear NLTS theorem
    arXiv.cs.CC Pub Date : 2020-11-03
    Anurag Anshu; Chinmay Nirkhe

    The No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings (Quantum Information and Computation, 2014) -- which posits the existence of a local Hamiltonian with a super-constant circuit lower bound on the complexity of all low-energy states -- identifies a fundamental obstacle to the resolution of the quantum PCP conjecture. In this paper, we provide new techniques, based on entropic

    更新日期:2020-11-05
  • The Complexity of Gradient Descent: CLS = PPAD $\cap$ PLS
    arXiv.cs.CC Pub Date : 2020-11-03
    John Fearnley; Paul W. Goldberg; Alexandros Hollender; Rahul Savani

    We study search problems that can be solved by performing Gradient Descent on a bounded convex polytopal domain and show that this class is equal to the intersection of two well-known classes: PPAD and PLS. As our main underlying technical contribution, we show that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain $[0,1]^2$ is PPAD $\cap$ PLS-complete

    更新日期:2020-11-04
  • The Complexity of Finding Fair Independent Sets in Cycles
    arXiv.cs.CC Pub Date : 2020-11-03
    Ishay Haviv

    Let $G$ be a cycle graph and let $V_1,\ldots,V_m$ be a partition of its vertex set into $m$ sets. An independent set $S$ of $G$ is said to fairly represent the partition if $|S \cap V_i| \geq \frac{1}{2} \cdot |V_i| -1$ for all $i \in [m]$. It is known that for every cycle and every partition of its vertex set, there exists an independent set that fairly represents the partition (Aharoni et al., A

    更新日期:2020-11-04
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
施普林格,自然编辑
ERIS期刊投稿
欢迎阅读创刊号
自然职场,为您触达千万科研人才
spring&清华大学出版社
城市可持续发展前沿研究专辑
Springer 纳米技术权威期刊征稿
全球视野覆盖
施普林格·自然新
chemistry
物理学研究前沿热点精选期刊推荐
自然职位线上招聘会
欢迎报名注册2020量子在线大会
化学领域亟待解决的问题
材料学研究精选新
GIANT
ACS ES&T Engineering
ACS ES&T Water
屿渡论文,编辑服务
ACS Publications填问卷
阿拉丁试剂right
苏州大学
林亮
南方科技大学
朱守非
胡少伟
有机所林亮
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
上海纽约大学
浙江大学
廖矿标
天合科研
x-mol收录
试剂库存
down
wechat
bug