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Related papers: Derandomizing HSSW Algorithm for 3-SAT

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The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…

Quantum Physics · Physics 2016-10-25 Niel de Beaudrap , Sevag Gharibian

We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems; 3-SAT is equivalent to…

Data Structures and Algorithms · Computer Science 2007-05-23 David Eppstein

In this paper, we devise three deterministic algorithms for solving the $m$-set $k$-packing, $m$-dimensional $k$-matching, and $t$-dominating set problems in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$ and $O^*(5.44^{t})$, respectively.…

Data Structures and Algorithms · Computer Science 2013-06-18 Shenshi Chen , Zhixiang Chen

We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >=…

Data Structures and Algorithms · Computer Science 2011-07-12 Marc Thurley

We show that the CNF satisfiability problem (SAT) can be solved in time $O^*(1.1199^{(d-2)n})$, where $d$ is either the maximum number of occurrences of any variable or the average number of occurrences of all variables if no variable…

Data Structures and Algorithms · Computer Science 2024-11-13 Sanjay Jain , Tzeh Yuan Neoh , Frank Stephan

The rigorous theoretical analyses of algorithms for exact 3-satisfiability (X3SAT) have been proposed in the literature. As we know, previous algorithms for solving X3SAT have been analyzed only regarding the number of variables as the…

Artificial Intelligence · Computer Science 2011-03-29 Junping Zhou , Minghao Yin

PPSZ, for long time the fastest known algorithm for $k$-SAT, works by going through the variables of the input formula in random order; each variable is then set randomly to $0$ or $1$, unless the correct value can be inferred by an…

Data Structures and Algorithms · Computer Science 2024-08-07 Dominik Scheder

We present an extremely simple polynomial-space exponential-time $(1-\varepsilon)$-approximation algorithm for MAX-k-SAT that is (slightly) faster than the previous known polynomial-space $(1-\varepsilon)$-approximation algorithms by Hirsch…

Data Structures and Algorithms · Computer Science 2026-04-22 Harry Buhrman , Sevag Gharibian , Zeph Landau , François Le Gall , Norbert Schuch , Suguru Tamaki

We revisit the 3SUM problem in the \emph{preprocessed universes} setting. We present an algorithm that, given three sets $A$, $B$, $C$ of $n$ integers, preprocesses them in quadratic time, so that given any subsets $A' \subseteq A$, $B'…

Data Structures and Algorithms · Computer Science 2025-10-22 Shashwat Kasliwal , Adam Polak , Pratyush Sharma

The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the…

Computational Complexity · Computer Science 2007-05-23 Tobias Riege , Jörg Rothe , Holger Spakowski , Masaki Yamamoto

A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…

Disordered Systems and Neural Networks · Physics 2009-11-07 W. Barthel , A. K. Hartmann , M. Leone , F. Ricci-Tersenghi , M. Weigt , R. Zecchina

Submodularity is one of the most important property of combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of $k$-submodular function is NP-hard, and approximation algorithms are studied. For…

Data Structures and Algorithms · Computer Science 2017-02-16 Hiroki Oshima

We reexamine the classical subset sum problem: given a set $X$ of $n$ positive integers and a number $t$, decide whether there exists a subset of $X$ that sums to $t$; or more generally, compute the set $\mbox{out}$ of all numbers…

Data Structures and Algorithms · Computer Science 2026-01-06 Timothy M. Chan

The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are…

Data Structures and Algorithms · Computer Science 2020-07-16 Gordon Hoi , Sanjay Jain , Frank Stephan

Three algorithms are presented that determine the existence of satisfying assignments for 3SAT Boolean satisfiability expressions. One algorithm is presented for determining an instance of a satisfying assignment, where such exists. The…

Computational Complexity · Computer Science 2019-12-16 Charles Sauerbier

This paper presents an algorithm for 3-SAT problems. First, logical formulas are transformed into elementary algebraic formulas. Second, complex trigonometric functions are assigned to the variables in the elementary algebraic formulas, and…

Data Structures and Algorithms · Computer Science 2017-08-01 Hiroshi Tsukimoto

In this paper, we examine the claims made by the paper "A polynomial-time algorithm for 3-SAT" by Lizhi Du. The paper claims to provide a polynomial-time algorithm for solving the NP-complete problem 3-SAT. In examining the paper's…

Computational Complexity · Computer Science 2024-04-09 Yumeng He , Matan Kotler-Berkowitz , Harry Liuson , Zeyu Nie

The method in this paper is wrong.

Computational Complexity · Computer Science 2012-10-19 Lily Chen

Using nuclear magnetic resonance (NMR) techniques with three-qubit sample, we have experimentally implemented the highly structured algorithm for the 1-SAT problem proposed by Hogg. A simplified temporal averaging procedure was employed to…

Quantum Physics · Physics 2009-11-07 Xinhua Peng , Xiwen Zhu , Ximing Fang , Mang Feng , Maili Liu , Kelin Gao

We present a new structural (or syntatic) approach for estimating the satisfiability threshold of random 3-SAT formulae. We show its efficiency in obtaining a jump from the previous upper bounds, lowering them to 4.506. The method combines…

Discrete Mathematics · Computer Science 2007-05-23 Olivier Dubois , Yacine Boufkhad , Jacques Mandler