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Compressed Communication Complexity of Hamming Distance arXiv.cs.CC Pub Date : 2021-03-05 Shiori Mitsuya; Yuto Nakashima; Shunsuke Inenaga; Hideo Bannai; Masayuki Takeda
We consider the communication complexity of the Hamming distance of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their strings in a compressed form, i.e., represented by the Lempel-Ziv 77 factorization (LZ77) with/without self-references. We present a randomized public-coin protocol
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On the Complexity of Equilibrium Computation in First-Price Auctions arXiv.cs.CC Pub Date : 2021-03-04 Aris Filos-Ratsikas; Yiannis Giannakopoulos; Alexandros Hollender; Philip Lazos; Diogo Poças
We consider the problem of computing a (pure) Bayes-Nash equilibrium in the first-price auction with continuous value distributions and discrete bidding space. We prove that when bidders have independent subjective prior beliefs about the value distributions of the other bidders, computing an $\varepsilon$-equilibrium of the auction is PPAD-complete, and computing an exact equilibrium is FIXP-complete
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Consensus in Blockchain Systems with Low Network Throughput: A Systematic Mapping Study arXiv.cs.CC Pub Date : 2021-03-04 Henrik Knudsen; Jakob Svennevik Notland; Peter Halland Haro; Truls Bakkejord Ræder; Jingyue Li
Blockchain technologies originate from cryptocurrencies. Thus, most blockchain technologies assume an environment with a fast and stable network. However, in some blockchain-based systems, e.g., supply chain management (SCM) systems, some Internet of Things (IOT) nodes can only rely on the low-quality network sometimes to achieve consensus. Thus, it is critical to understand the applicability of existing
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Incidence geometry in the projective plane via almost-principal minors of symmetric matrices arXiv.cs.CC Pub Date : 2021-03-03 Tobias Boege
We present an encoding of a polynomial system into vanishing and non-vanishing constraints on almost-principal minors of a symmetric, principally regular matrix, such that the solvability of the system over some field is equivalent to the satisfiability of the constraints over that field. This implies two complexity results about Gaussian conditional independence structures. First, all real algebraic
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Separating ABPs and Some Structured Formulas in the Non-Commutative Setting arXiv.cs.CC Pub Date : 2021-03-01 Prerona Chatterjee
The motivating question for this work is a long standing open problem, posed by Nisan (1991), regarding the relative powers of algebraic branching programs (ABPs) and formulas in the non-commutative setting. Even though the general question continues to remain open, we make some progress towards its resolution. To that effect, we generalise the notion of ordered polynomials in the non-commutative setting
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How do exponential size solutions arise in semidefinite programming? arXiv.cs.CC Pub Date : 2021-02-26 Gábor Pataki; Aleksandr Touzov
As a classic example of Khachiyan shows, some semidefinite programs (SDPs) have solutions whose size -- the number of bits necessary to describe them -- is exponential in the size of the input. Exponential size solutions are the main obstacle to solve a long standing open problem: can we decide feasibility of SDPs in polynomial time? We prove that large solutions are actually quite common in SDPs:
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Can Romeo and Juliet Meet? Or Rendezvous Games with Adversaries on Graphs arXiv.cs.CC Pub Date : 2021-02-26 Fedor V. Fomin; Petr A. Golovach; Dimitrios M. Thilikos
We introduce the rendezvous game with adversaries. In this game, two players, {\sl Facilitator} and {\sl Disruptor}, play against each other on a graph. Facilitator has two agents, and Disruptor has a team of $k$ agents located in some vertices of the graph. They take turns in moving their agents to adjacent vertices (or staying). Facilitator wins if his agents meet in some vertex of the graph. The
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Many-Qudit representation for the Travelling Salesman Problem Optimisation arXiv.cs.CC Pub Date : 2021-02-26 Vladimir Vargas-Calderón; Nicolas Parra-A.; Herbert Vinck-Posada; Fabio A. González
We present a map from the travelling salesman problem (TSP), a prototypical NP-complete combinatorial optimisation task, to the ground state associated with a system of many-qudits. Conventionally, the TSP is cast into a quadratic unconstrained binary optimisation (QUBO) problem, that can be solved on an Ising machine. The size of the corresponding physical system's Hilbert space is $2^{N^2}$, where
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Semidefinite Relaxations of Products of Nonnegative Forms on the Sphere arXiv.cs.CC Pub Date : 2021-02-25 Chenyang Yuan; Pablo A. Parrilo
We study the problem of maximizing the geometric mean of $d$ low-degree non-negative forms on the real or complex sphere in $n$ variables. We show that this highly non-convex problem is NP-hard even when the forms are quadratic and is equivalent to optimizing a homogeneous polynomial of degree $O(d)$ on the sphere. The standard Sum-of-Squares based convex relaxation for this polynomial optimization
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A Comprehensive Survey on the Multiple Travelling Salesman Problem: Applications, Approaches and Taxonomy arXiv.cs.CC Pub Date : 2021-02-25 Omar Cheikhrouhou; Ines Khoufi
The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc. Although the importance of this optimization problem, there is no survey dedicated to reviewing recent MTSP contributions. In this paper, we aim to fill this gap by providing a comprehensive
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Subcubic Certificates for CFL Reachability arXiv.cs.CC Pub Date : 2021-02-25 Dmitry Chistikov; Rupak Majumdar; Philipp Schepper
Many problems in interprocedural program analysis can be modeled as the context-free language (CFL) reachability problem on graphs and can be solved in cubic time. Despite years of efforts, there are no known truly sub-cubic algorithms for this problem. We study the related certification task: given an instance of CFL reachability, are there small and efficiently checkable certificates for the existence
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Algorithms and Complexity on Indexing Founder Graphs arXiv.cs.CC Pub Date : 2021-02-25 Massimo Equi; Tuukka Norri; Jarno Alanko; Bastien Cazaux; Alexandru I. Tomescu; Veli Mäkinen
We introduce a compact pangenome representation based on an optimal segmentation concept that aims to reconstruct founder sequences from a multiple sequence alignment (MSA). Such founder sequences have the feature that each row of the MSA is a recombination of the founders. Several linear time dynamic programming algorithms have been previously devised to optimize segmentations that induce founder
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Classification of the streaming approximability of Boolean CSPs arXiv.cs.CC Pub Date : 2021-02-24 Chi-Ning Chou; Alexander Golovnev; Madhu Sudan; Santhoshini Velusamy
A Boolean constraint satisfaction problem (CSP), Max-CSP$(f)$, is a maximization problem specified by a constraint $f:\{-1,1\}^k\to\{0,1\}$. An instance of the problem consists of $m$ constraint applications on $n$ Boolean variables, where each constraint application applies the constraint to $k$ literals chosen from the $n$ variables and their negations. The goal is to compute the maximum number of
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Optimal Control Policies to Address the Pandemic Health-Economy Dilemma arXiv.cs.CC Pub Date : 2021-02-24 Rohit Salgotra; Thomas Seidelmann; Dominik Fischer; Sanaz Mostaghim; Amiram Moshaiov
Non-pharmaceutical interventions (NPIs) are effective measures to contain a pandemic. Yet, such control measures commonly have a negative effect on the economy. Here, we propose a macro-level approach to support resolving this Health-Economy Dilemma (HED). First, an extension to the well-known SEIR model is suggested which includes an economy model. Second, a bi-objective optimization problem is defined
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Kronecker Products, Low-Depth Circuits, and Matrix Rigidity arXiv.cs.CC Pub Date : 2021-02-24 Josh Alman
For a matrix $M$ and a positive integer $r$, the rank $r$ rigidity of $M$ is the smallest number of entries of $M$ which one must change to make its rank at most $r$. There are many known applications of rigidity lower bounds to a variety of areas in complexity theory, but fewer known applications of rigidity upper bounds. In this paper, we use rigidity upper bounds to prove new upper bounds in a few
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Being correct is not enough: efficient verification using robust linear temporal logic arXiv.cs.CC Pub Date : 2021-02-24 Tzanis Anevlavis; Matthew Philippe; Daniel Neider; Paulo Tabuada
While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we introduce the logic rLTL which provides a means to formally reason about both correctness and robustness in system design. Furthermore, we identify a large fragment of rLTL for which the verification problem can be efficiently solved, i.e., verification can be done by using
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Conditional Dichotomy of Boolean Ordered Promise CSPs arXiv.cs.CC Pub Date : 2021-02-23 Joshua Brakensiek; Venkatesan Guruswami; Sai Sandeep
Promise Constraint Satisfaction Problems (PCSPs) are a generalization of Constraint Satisfaction Problems (CSPs) where each predicate has a strong and a weak form and given a CSP instance, the objective is to distinguish if the strong form can be satisfied vs. even the weak form cannot be satisfied. Since their formal introduction by Austrin, Guruswami, and H\aa stad, there has been a flurry of works
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Parameterized Complexity of Logic-Based Argumentation in Schaefer's Framework arXiv.cs.CC Pub Date : 2021-02-23 Yasir Mahmood; Arne Meier; Johannes Schmidt
Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent, subset-minimal, and implies the claim. In such a case, the pair of the support and the claim together is called an argument. In this paper, we study the propositional variants
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Functional norms, condition numbers and numerical algorithms in algebraic geometry arXiv.cs.CC Pub Date : 2021-02-23 Felipe Cucker; Alperen A. Ergür; Josué Tonelli-Cueto
In numerical linear algebra, a well-established practice is to choose a norm that exploits the structure of the problem at hand in order to optimize accuracy or computational complexity. In numerical polynomial algebra, a single norm (attributed to Weyl) dominates the literature. This article initiates the use of $L_p$ norms for numerical algebraic geometry, with an emphasis on $L_{\infty}$. This classical
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Optimal Sorting Circuits for Short Keys arXiv.cs.CC Pub Date : 2021-02-23 Wei-Kai Lin; Elaine Shi
A long-standing open question in the algorithms and complexity literature is whether there exist sorting circuits of size $o(n \log n)$. A recent work by Asharov, Lin, and Shi (SODA'21) showed that if the elements to be sorted have short keys whose length $k = o(\log n)$, then one can indeed overcome the $n\log n$ barrier for sorting circuits, by leveraging non-comparison-based techniques. More specifically
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Quantum query complexity with matrix-vector products arXiv.cs.CC Pub Date : 2021-02-22 Andrew M. Childs; Shih-Han Hung; Tongyang Li
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear system that it specifies, quantum computers do not provide an asymptotic speedup over classical computation. On the other hand, we show that for some problems, such
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Near-Optimal Two-Pass Streaming Algorithm for Sampling Random Walks over Directed Graphs arXiv.cs.CC Pub Date : 2021-02-22 Lijie Chen; Gillat Kol; Dmitry Paramonov; Raghuvansh Saxena; Zhao Song; Huacheng Yu
For a directed graph $G$ with $n$ vertices and a start vertex $u_{\sf start}$, we wish to (approximately) sample an $L$-step random walk over $G$ starting from $u_{\sf start}$ with minimum space using an algorithm that only makes few passes over the edges of the graph. This problem found many applications, for instance, in approximating the PageRank of a webpage. If only a single pass is allowed, the
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TS-Reconfiguration of Dominating Sets in circle and circular-arc graphs arXiv.cs.CC Pub Date : 2021-02-21 Nicolas Bousquet; Alice Joffard
We study the dominating set reconfiguration problem with the token sliding rule. It consists, given a graph G=(V,E) and two dominating sets D_s and D_t of G, in determining if there exists a sequence S= of dominating sets of G such that for any two consecutive dominating sets D_r and D_{r+1} with r
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An Optimal Inverse Theorem arXiv.cs.CC Pub Date : 2021-02-21 Alex Cohen; Guy Moshkovitz
We prove that the partition rank and the analytic rank of tensors are equal up to a constant, over any large enough finite field. The proof constructs rational maps computing a partition rank decomposition for successive derivatives of the tensor, on an open subset of the kernel variety associated with the tensor. This largely settles the main question in the "bias implies low rank" line of work in
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Sorting Short Integers arXiv.cs.CC Pub Date : 2021-02-19 Michal Koucký; Karel Král
We build boolean circuits of size $O(nm^2)$ and depth $O(\log(n) + m \log(m))$ for sorting $m$-bit itnegers. We build also circuits that sort $m$-bit integers according to their first $k$ bits that are of size $O(nmk(1 + \log^*(n) - \log^*(m)))$ and depth $O(\log^{3.1} n)$. This improves on the result of Asharov et al. arXiv:2010.09884 and resolves some of their open questions.
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Parallel algorithms for power circuits and the word problem of the Baumslag group arXiv.cs.CC Pub Date : 2021-02-19 Caroline Mattes; Armin Weiß
Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and $(x,y) \mapsto x2^y$. The same authors applied power circuits to give a polynomial-time solution to the word problem of the Baumslag group, which has a non-elementary Dehn function. In this work, we examine power circuits
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Training Neural Networks is ER-complete arXiv.cs.CC Pub Date : 2021-02-19 Mikkel Abrahamsen; Linda Kleist; Tillmann Miltzow
Given a neural network, training data, and a threshold, it was known that it is NP-hard to find weights for the neural network such that the total error is below the threshold. We determine the algorithmic complexity of this fundamental problem precisely, by showing that it is ER-complete. This means that the problem is equivalent, up to polynomial-time reductions, to deciding whether a system of polynomial
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Data Structures Lower Bounds and Popular Conjectures arXiv.cs.CC Pub Date : 2021-02-18 Pavel Dvořák; Michal Koucký; Karel Král; Veronika Slívová
In this paper, we investigate the relative power of several conjectures that attracted recently lot of interest. We establish a connection between the Network Coding Conjecture (NCC) of Li and Li and several data structure like problems such as non-adaptive function inversion of Hellman and the well-studied problem of polynomial evaluation and interpolation. In turn these data structure problems imply
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Classically Verifiable (Dual-Mode) NIZK for QMA with Preprocessing arXiv.cs.CC Pub Date : 2021-02-18 Tomoyuki Morimae; Takashi Yamakawa
We propose three constructions of classically verifiable non-interactive proofs (CV-NIP) and non-interactive zero-knowledge proofs and arguments (CV-NIZK) for QMA in various preprocessing models. - We construct an information theoretically sound CV-NIP for QMA in the secret parameter model where a trusted party generates a quantum proving key and classical verification key and gives them to the corresponding
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Deterministic Algorithms for Compiling Quantum Circuits with Recurrent Patterns arXiv.cs.CC Pub Date : 2021-02-17 Davide Ferrari; Ivano Tavernelli; Michele Amoretti
Current quantum processors are noisy, have limited coherence and imperfect gate implementations. On such hardware, only algorithms that are shorter than the overall coherence time can be implemented and executed successfully. A good quantum compiler must translate an input program into the most efficient equivalent of itself, getting the most out of the available hardware. In this work, we present
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Local Mending arXiv.cs.CC Pub Date : 2021-02-17 Alkida Balliu; Juho Hirvonen; Darya Melnyk; Dennis Olivetti; Joel Rybicki; Jukka Suomela
In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a hole." We explore how mendability is connected to the existence of efficient algorithms, especially in distributed, parallel, and fault-tolerant settings. It is easy
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Unambiguous DNFs from Hex arXiv.cs.CC Pub Date : 2021-02-16 Shalev Ben-David; Mika Göös; Siddhartha Jain; Robin Kothari
We exhibit an unambiguous k-DNF formula that requires CNF width Omega~(k^{1.5}). Our construction is inspired by the board game Hex and it is vastly simpler than previous ones, which achieved at best an exponent of 1.22. Our result is known to imply several other improved separations in query and communication complexity (e.g., clique vs. independent set problem) and graph theory (Alon--Saks--Seymour
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Depth lower bounds in Stabbing Planes for combinatorial principles arXiv.cs.CC Pub Date : 2021-02-15 Stefan Dantchev; Nicola Galesi; Abdul Ghani; Barnaby Martin
We prove logarithmic depth lower bounds in Stabbing Planes for the classes of combinatorial principles known as the Pigeonhole principle and the Tseitin contradictions. The depth lower bounds are new, obtained by giving almost linear length lower bounds which do not depend on the bit-size of the inequalities and in the case of the Pigeonhole principle are tight. The technique known so far to prove
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A note on VNP-completeness and border complexity arXiv.cs.CC Pub Date : 2021-02-14 Christian Ikenmeyer; Abhiroop Sanyal
In 1979 Valiant introduced the complexity class VNP of p-definable families of polynomials, he defined the reduction notion known as p-projection and he proved that the permanent polynomial and the Hamiltonian cycle polynomial are VNP-complete under p-projections. In 2001 Mulmuley and Sohoni (and independently B\"urgisser) introduced the notion of border complexity to the study of the algebraic complexity
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Lower Bounds on Dynamic Programming for Maximum Weight Independent Set arXiv.cs.CC Pub Date : 2021-02-13 Tuukka Korhonen
We prove lower bounds on pure dynamic programming algorithms for maximum weight independent set (MWIS). We model such algorithms as tropical circuits, i.e., circuits that compute with $\max$ and $+$ operations. For a graph $G$, an MWIS-circuit of $G$ is a tropical circuit whose inputs correspond to vertices of $G$ and which computes the weight of a maximum weight independent set of $G$ for any assignment
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Comprehensive Comparative Study of Multi-Label Classification Methods arXiv.cs.CC Pub Date : 2021-02-14 Jasmin Bogatinovski; Ljupčo Todorovski; Sašo Džeroski; Dragi Kocev
Multi-label classification (MLC) has recently received increasing interest from the machine learning community. Several studies provide reviews of methods and datasets for MLC and a few provide empirical comparisons of MLC methods. However, they are limited in the number of methods and datasets considered. This work provides a comprehensive empirical study of a wide range of MLC methods on a plethora
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Optimal Streaming Algorithms for Graph Matching arXiv.cs.CC Pub Date : 2021-02-13 Jianer Chen; Qin Huang; Iyad Kanj; Ge Xia
We present parameterized streaming algorithms for the graph matching problem in both the dynamic and the insert-only models. For the dynamic streaming model, we present a one-pass algorithm that, with high probability, computes a maximum-weight $k$-matching of a weighted graph in $\tilde{O}(Wk^2)$ space and that has $\tilde{O}(1)$ update time, where $W$ is the number of distinct edge weights and the
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Interactive quantum advantage with noisy, shallow Clifford circuits arXiv.cs.CC Pub Date : 2021-02-13 Daniel Grier; Nathan Ju; Luke Schaeffer
Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC$^0$) can solve with near certainty (probability $1 - o(1)$), but that any bounded fan-in constant-depth classical circuit (NC$^0$) fails with some constant probability. We show that this robustness to noise can be achieved in the other low-depth quantum/classical circuit separations in this area
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The Complexity of Transitively Orienting Temporal Graphs arXiv.cs.CC Pub Date : 2021-02-12 George B. Mertzios; Hendrik Molter; Malte Renken; Paul G. Spirakis; Philipp Zschoche
In a temporal network with discrete time-labels on its edges, entities and information can only "flow" along sequences of edges whose time-labels are non-decreasing (resp. increasing), i.e. along temporal (resp. strict temporal) paths. Nevertheless, in the model for temporal networks of [Kempe et al., JCSS, 2002], the individual time-labeled edges remain undirected: an edge $e=\{u,v\}$ with time-label
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Proof complexity of positive branching programs arXiv.cs.CC Pub Date : 2021-02-12 Anupam Das; Avgerinos Delkos
We investigate the proof complexity of systems based on positive branching programs, i.e. non-deterministic branching programs (NBPs) where, for any 0-transition between two nodes, there is also a 1-transition. Positive NBPs compute monotone Boolean functions, just like negation-free circuits or formulas, but constitute a positive version of (non-uniform) NL, rather than P or NC1, respectively. The
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Barriers for recent methods in geodesic optimization arXiv.cs.CC Pub Date : 2021-02-12 Cole Franks; Philipp Reichenbach
We study a class of optimization problems including matrix scaling, matrix balancing, multidimensional array scaling, operator scaling, and tensor scaling that arise frequently in theory and in practice. Some of these problems, such as matrix and array scaling, are convex in the Euclidean sense, but others such as operator scaling and tensor scaling are \emph{geodesically convex} on a different Riemannian
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ReLU Neural Networks for Exact Maximum Flow Computation arXiv.cs.CC Pub Date : 2021-02-12 Christoph Hertrich; Leon Sering
Understanding the great empirical success of artificial neural networks (NNs) from a theoretical point of view is currently one of the hottest research topics in computer science. In this paper we study the expressive power of NNs with rectified linear units from a combinatorial optimization perspective. In particular, we show that, given a directed graph with $n$ nodes and $m$ arcs, there exists an
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Algorithms, Reductions and Equivalences for Small Weight Variants of All-Pairs Shortest Paths arXiv.cs.CC Pub Date : 2021-02-11 Timothy M. Chan; Virginia Vassilevska Williams; Yinzhan Xu
APSP with small integer weights in undirected graphs [Seidel'95, Galil and Margalit'97] has an $\tilde{O}(n^\omega)$ time algorithm, where $\omega<2.373$ is the matrix multiplication exponent. APSP in directed graphs with small weights however, has a much slower running time that would be $\Omega(n^{2.5})$ even if $\omega=2$ [Zwick'02]. To understand this $n^{2.5}$ bottleneck, we build a web of reductions
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Hitting Sets and Reconstruction for Dense Orbits in $\text{VP}_e$ and $ΣΠΣ$ Circuits arXiv.cs.CC Pub Date : 2021-02-10 Dori Medini; Amir Shpilka
In this paper we study polynomials in $\text{VP}_e$ (polynomial-sized formulas) and in $\Sigma\Pi\Sigma$ (polynomial-size depth-$3$ circuits) whose orbits, under the action of the affine group $\text{GL}_n^{\text{aff}}(\mathbb{F})$, are $\mathit{dense}$ in their ambient class. We construct hitting sets and interpolating sets for these orbits as well as give reconstruction algorithms. As $\text{VP}=\text{VNC}^2$
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Slicing the hypercube is not easy arXiv.cs.CC Pub Date : 2021-02-10 Gal Yehuda; Amir Yehudayoff
We prove that at least $\Omega(n^{0.51})$ hyperplanes are needed to slice all edges of the $n$-dimensional hypercube. We provide a couple of applications: lower bounds on the computational complexity of parity, and a lower bound on the cover number of the hypercube by skew hyperplanes.
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On the Power and Limitations of Branch and Cut arXiv.cs.CC Pub Date : 2021-02-09 Noah Fleming; Mika Göös; Russell Impagliazzo; Toniann Pitassi; Robert Robere; Li-Yang Tan; Avi Wigderson
The Stabbing Planes proof system was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formulas -- certain unsatisfiable systems of linear equations mod 2 -- which are canonical hard examples for many algebraic proof systems. In a recent (and surprising) result,
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On Computation Complexity of True Proof Number Search arXiv.cs.CC Pub Date : 2021-02-08 Chao Gao
We point out that the computation of true \emph{proof} and \emph{disproof} numbers for proof number search in arbitrary directed acyclic graphs is NP-hard, an important theoretical result for proof number search. The proof requires a reduction from SAT, which demonstrates that finding true proof/disproof number for arbitrary DAG is at least as hard as deciding if arbitrary SAT instance is satisfiable
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Constant Approximating k-Clique is W[1]-hard arXiv.cs.CC Pub Date : 2021-02-09 Bingkai Lin
For every graph $G$, let $\omega(G)$ be the largest size of complete subgraph in $G$. This paper presents a simple algorithm which, on input a graph $G$, a positive integer $k$ and a small constant $\epsilon>0$, outputs a graph $G'$ and an integer $k'$ in $2^{\Theta(k^5)}\cdot |G|^{O(1)}$-time such that (1) $k'\le 2^{\Theta(k^5)}$, (2) if $\omega(G)\ge k$, then $\omega(G')\ge k'$, (3) if $\omega(G)
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Placing Green Bridges Optimally, with a Multivariate Analysis arXiv.cs.CC Pub Date : 2021-02-08 Till Fluschnik; Leon Kellerhals
We study the problem of placing wildlife crossings, such as green bridges, over human-made obstacles to challenge habitat fragmentation. The main task herein is, given a graph describing habitats or routes of wildlife animals and possibilities of building green bridges, to find a low-cost placement of green bridges that connects the habitats. We develop different problem models for this task and study
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Attention-Based Neural Networks for Chroma Intra Prediction in Video Coding arXiv.cs.CC Pub Date : 2021-02-09 Marc Górriz; Saverio Blasi; Alan F. Smeaton; Noel E. O'Connor; Marta Mrak
Neural networks can be successfully used to improve several modules of advanced video coding schemes. In particular, compression of colour components was shown to greatly benefit from usage of machine learning models, thanks to the design of appropriate attention-based architectures that allow the prediction to exploit specific samples in the reference region. However, such architectures tend to be
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Approximately counting independent sets of a given size in bounded-degree graphs arXiv.cs.CC Pub Date : 2021-02-09 Ewan Davies; Will Perkins
We determine the computational complexity of approximately counting and sampling independent sets of a given size in bounded-degree graphs. That is, we identify a critical density $\alpha_c(\Delta)$ and provide (i) for $\alpha < \alpha_c(\Delta)$ randomized polynomial-time algorithms for approximately sampling and counting independent sets of given size at most $\alpha n$ in $n$-vertex graphs of maximum
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Inapproximability of Minimizing a Pair of DNFs or Binary Decision Trees Defining a Partial Boolean Function arXiv.cs.CC Pub Date : 2021-02-09 David Stein; Bjoern Andres
The desire to apply machine learning techniques in safety-critical environments has renewed interest in the learning of partial functions for distinguishing between positive, negative and unclear observations. We contribute to the understanding of the hardness of this problem. Specifically, we consider partial Boolean functions defined by a pair of Boolean functions $f, g \colon \{0,1\}^J \to \{0,1\}$
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Structure vs. Randomness for Bilinear Maps arXiv.cs.CC Pub Date : 2021-02-09 Alex Cohen; Guy Moshkovitz
We prove that the slice rank of a 3-tensor (a combinatorial notion introduced by Tao in the context of the cap-set problem), the analytic rank (a Fourier-theoretic notion introduced by Gowers and Wolf), and the geometric rank (a recently introduced algebro-geometric notion) are all equivalent up to an absolute constant. As a corollary, we obtain strong trade-offs on the arithmetic complexity of a biased
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A full complexity dichotomy for immanant families arXiv.cs.CC Pub Date : 2021-02-08 Radu Curticapean
Given an integer $n\geq 1$ and an irreducible character $\chi_{\lambda}$ of $S_{n}$ for some partition $\lambda$ of $n$, the immanant $\mathrm{imm}_{\lambda}:\mathbb{C}^{n\times n}\to\mathbb{C}$ maps matrices $A\in\mathbb{C}^{n\times n}$ to $\mathrm{imm}_{\lambda}(A)=\sum_{\pi\in S_{n}}\chi_{\lambda}(\pi)\prod_{i=1}^{n}A_{i,\pi(i)}$. Important special cases include the determinant and permanent, which
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Enumerating maximal consistent closed sets in closure systems arXiv.cs.CC Pub Date : 2021-02-05 Lhouari Nourine; Simon Vilmin
Given an implicational base, a well-known representation for a closure system, an inconsistency binary relation over a finite set, we are interested in the problem of enumerating all maximal consistent closed sets (denoted by MCCEnum for short). We show that MCCEnum cannot be solved in output-polynomial time unless $\textsf{P} = \textsf{NP}$, even for lower bounded lattices. We give an incremental-polynomial
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Quantum Algorithmic Information Theory arXiv.cs.CC Pub Date : 2021-02-07 Samuel Epstein
This paper extends quantum information theory into the algorithmic sphere, using randomness and information conservation inequalities. We show for an overwhelming majority of pure states, the self classical algorithmic information induced by a measurement will be negligible. Purification of two states increases information. Decoherence causes quantum states to lose information with all other quantum
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Parameterized Complexity of Immunization in the Threshold Model arXiv.cs.CC Pub Date : 2021-02-06 Gennaro Cordasco; Luisa Gargano; Adele Anna Rescigno
We consider the problem of controlling the spread of harmful items in networks, such as the contagion proliferation of diseases or the diffusion of fake news. We assume the linear threshold model of diffusion where each node has a threshold that measures the node resistance to the contagion. We study the parameterized complexity of the problem: Given a network, a set of initially contaminated nodes
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A Dynamic Data Structure for Temporal Reachability with Unsorted Contact Insertions arXiv.cs.CC Pub Date : 2021-02-08 Luiz F. Afra Brito; Marcelo Albertini; Arnaud Casteigts; Bruno A. N. Travençolo
Temporal graphs represent interactions between entities over the time. These interactions may be direct (a contact between two nodes at some time instant), or indirect, through sequences of contacts called temporal paths (journeys). Deciding whether an entity can reach another through a journey is useful for various applications in communication networks and epidemiology, among other fields. In this
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A Knowledge Compilation Map for Conditional Preference Statements-based Languages arXiv.cs.CC Pub Date : 2021-02-08 Hélène FargierIRIT-ADRIA; Jérôme MenginIRIT-ADRIA
Conditional preference statements have been used to compactly represent preferences over combinatorial domains. They are at the core of CP-nets and their generalizations, and lexicographic preference trees. Several works have addressed the complexity of some queries (optimization, dominance in particular). We extend in this paper some of these results, and study other queries which have not been addressed
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Parameterized complexity of computing maximum minimal blocking and hitting sets arXiv.cs.CC Pub Date : 2021-02-05 Júlio Araújo; Marin Bougeret; Victor A. Campos; Ignasi Sau
A blocking set in a graph $G$ is a subset of vertices that intersects every maximum independent set of $G$. Let ${\sf mmbs}(G)$ be the size of a maximum (inclusion-wise) minimal blocking set of $G$. This parameter has recently played an important role in the kernelization of Vertex Cover parameterized by the distance to a graph class ${\cal F}$. Indeed, it turns out that the existence of a polynomial
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