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An Improved Exact Algorithm for the Exact Satisfiability Problem
[article]

2020
*
arXiv
*
pre-print

Since it is

arXiv:2010.03850v3
fatcat:d7mlnhplnja45kwdixmywh2zoa
*an*important variant of*the**satisfiability**problem*, XSAT has also been studied heavily and has seen numerous*improvements*to*the*development of its*exact**algorithms*over*the*years. ...*The**Exact**Satisfiability**problem*, XSAT, is defined as*the**problem*of finding a*satisfying*assignment to a formula φ in CNF such that exactly one literal in each clause is assigned to be "1" and*the*other ... One such important variant is*the**Exact**Satisfiability**problem*, XSAT, where it asks if one can find a*satisfying*assignment such that exactly one of*the*literal in each clause is assigned*the*value "1" ...##
###
Exact Algorithms for NP-Hard Problems: A Survey
[chapter]

2003
*
Lecture Notes in Computer Science
*

*The*list of discussed NP-complete

*problems*includes

*the*travelling salesman

*problem*, scheduling under precedence constraints,

*satisfiability*, knapsack, graph coloring, independent sets in graphs, bandwidth ... We discuss fast exponential time solutions

*for*NP-complete

*problems*. We survey known results and approaches, we provide pointers to

*the*literature, and we discuss several open

*problems*in this area. ... Furthermore, I thank

*an*unknown referee

*for*many suggestions how to

*improve*

*the*structure,

*the*English,

*the*style, and

*the*contents of this paper. ...

##
###
Guest Editorial: Special Issue on Parameterized and Exact Computation, Part I

2011
*
Algorithmica
*

In particular,

doi:10.1007/s00453-011-9605-3
fatcat:5bwu4ykmlrcypdm5wzdvtehirq
*for*hard*problems*,*the*aim is to confine*the*combinatorial explosion of*the*running time of*the**algorithms*to small parameters in*the*input. ... While some of these are selected and extended papers from International Symposium on Parameterized and*Exact*Computation (IPEC) 2010,*the*rest were selected from*the*submissions received*for*our call*for*... one gives*an**improved*fixed-parameter tractable*algorithm*and*an**improved*kernel*for**the*pathwidth one deletion*problem*(can we delete at most k vertices to obtain a graph of pathwidth at most one). ...##
###
Using CSP To Improve Deterministic 3-SAT
[article]

2010
*
arXiv
*
pre-print

This way, we

arXiv:1007.1166v2
fatcat:ym467qyej5g2zh7tblo2ven2eq
*improve**the*deterministic worst-case running time*for*3-SAT to O(1.439^n). ... We show how one can use certain deterministic*algorithms**for*higher-value constraint satisfaction*problems*(CSPs) to speed up deterministic local search*for*3-SAT. ... Together with*An**Improved**Algorithm**for*Ball-3-SAT In this section we will describe*an**algorithm**for*Ball-3-SAT. ...##
###
An Improved Exact Algorithm for the Domatic Number Problem
[article]

2006
*
arXiv
*
pre-print

To prove our result, we combine

arXiv:cs/0603060v1
fatcat:tthcokzv7fe53h4gwwasry3jky
*an**algorithm*by Fomin et al. with Yamamoto's*algorithm**for**the**satisfiability**problem*. ... In addition, we show that*the*3-domatic number*problem*can be solved*for*graphs G with bounded maximum degree Delta(G) by a randomized*algorithm*, whose running time is better than*the*previous bound due ... We are grateful to Osamu Watanabe and Dieter Kratsch*for*inspiring discussions on*the*subject of this paper. In particular, we thank Dieter Kratsch*for*calling our attention to Lawler's*algorithm*. ...##
###
Optimal power flow in direct current networks

2013
*
52nd IEEE Conference on Decision and Control
*

In this paper, we study

doi:10.1109/cdc.2013.6760774
dblp:conf/cdc/GanL13
fatcat:7maq55kqazdkpklwqv7ncxwd64
*the*OPF*problem*in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered*for*solving*the*OPF*problem*. ... Based on 1), a modified OPF*problem*is proposed, whose corresponding SOCP is guaranteed to be*exact*. We also prove that SOCP has at most one optimal solution if it is*exact*. ... Section IV provides sufficient conditions*for**the**exactness*of*the*SOCP relaxation, and Section V proposes a modified OPF*problem*that always has*an**exact*SOCP relaxation. ...##
###
Optimal Power Flow in Direct Current Networks

2014
*
IEEE Transactions on Power Systems
*

In this paper, we study

doi:10.1109/tpwrs.2014.2313514
fatcat:y5hqnpg26rf3pj3j5ox3yhro3a
*the*OPF*problem*in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered*for*solving*the*OPF*problem*. ... Based on 1), a modified OPF*problem*is proposed, whose corresponding SOCP is guaranteed to be*exact*. We also prove that SOCP has at most one optimal solution if it is*exact*. ... Section IV provides sufficient conditions*for**the**exactness*of*the*SOCP relaxation, and Section V proposes a modified OPF*problem*that always has*an**exact*SOCP relaxation. ...##
###
Discrete Artificial Dragonflies Algorithm in Agent Based Modelling for Exact Boolean kSatisfiability Problem

2020
*
Journal of Advances in Mathematics and Computer Science
*

*the*states of neurons,

*for*optimal Boolean

*Exact*

*Satisfiability*representation on NETLOGO as a dynamic platform. ...

*satisfiability*

*problem*is better than existing methods in

*the*literature. ... Since

*the*original version of dragonfly

*algorithm*worked

*for*continuous optimization

*problems*, and

*the*

*Exact*kSatisfiability

*problem*is considered as a discrete optimization

*problem*. ...

##
###
Parameterized Inapproximability of Exact Cover and Nearest Codeword
[article]

2019
*
arXiv
*
pre-print

We prove that, assuming ETH,

arXiv:1905.06503v2
fatcat:ewnbq3n4dzfjjauovlj7yv52o4
*for*some $\gamma > 0$ there is no time $f(k) \cdot N^{\gamma k}$*algorithm*that can, given a $k$-ExactCover instance $I$, distinguish between*the*case where $I$ has*an**exact*...*The*$k$-ExactCover*problem*is a parameterized version of*the*ExactCover*problem*, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and*an*integer $k$, and*the*task is to determine ... We thank Pasin Manurangsi*for*some useful discussions on ExactCover and*the*recent literature in parameterized inapproximability. ...##
###
Approximating MAX SAT by moderately exponential and parameterized algorithms

2014
*
Theoretical Computer Science
*

We study approximation of

doi:10.1016/j.tcs.2014.10.039
fatcat:p4spt2lilzgb3kgxqwzbws3ncm
*the*max sat*problem*by moderately exponential*algorithms*. ... than those needed*for**exact*computation, approximation ratios unachievable in polynomial time. ... This kind of reduction from*an*approximate solution to*an**exact*one would allow to take advantage of any possible*improvement*of*the**exact*solution of max sat, which is not*the*case in*Algorithm*6. ...##
###
Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints
[article]

2014
*
arXiv
*
pre-print

Our

arXiv:1405.6851v2
fatcat:ajyhfho7jvhe5oh5puxl6o2dcm
*algorithms*are quadratically faster than exhaustive search and almost quadratically faster than*an**algorithm**for**an*inequality version of*the**problem*by Impagliazzo, Lovett, Paturi and Schneider (arXiv ... Rather than*improving**the*time and space complexity, we advance to a simple direction as inclusion of many NP-hard*problems*in terms of*exact*exponential*algorithms*. ...*the**exact**satisfiability**problem*[5] and*the**exact*hitting set*problem*[7] ) have*algorithms*faster than O(1.415 n )-time. ...##
###
On the Parameterized Complexity of Exact Satisfiability Problems
[chapter]

2005
*
Lecture Notes in Computer Science
*

*For*many

*problems*,

*the*investigation of their parameterized complexity provides

*an*interesting and useful point of view. ...

*The*most obvious natural parameterization

*for*

*the*maximum

*satisfiability*

*problem*-

*the*number of

*satisfiable*clauses-makes little sense, because at least half of

*the*clauses can be

*satisfied*in any formula ... We would like to thank several anonymous referees

*for*helpful comments, especially regarding

*the*final section. ...

##
###
Confronting hardness using a hybrid approach

2006
*
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
*

*an*approximation ratio exceeding that of

*the*known or conjectured inapproximability of

*the*

*problem*, assuming P = NP. ... each heuristic h i of

*the*hybrid

*algorithm*, one can give a complexity guarantee

*for*h i on

*the*instances of Π that S selects

*for*h i that is strictly better than m i . ... Uriel Feige's suggestions on

*the*minimum bandwidth

*problem*are highly appreciated.

*The*authors also thank past anonymous reviewers

*for*helpful comments. ...

##
###
Page 119 of The Journal of the Operational Research Society Vol. 59, Issue 1
[page]

2008
*
The Journal of the Operational Research Society
*

*An*

*exact*

*algorithm*is necessary

*for*

*the*following reasons even if

*the*

*problem*was proven to be NP-hard in Sung and Song (2003). ... Second,

*an*

*exact*

*algorithm*may provide a strong basis to evaluate

*the*performance of any other heuristics

*for*

*the*

*problem*(CDSCNDP). ...

##
###
A Hybrid Quantum Genetic Algorithm and Local Search based DPLL for Max 3-SAT Problems

2014
*
Applied Mathematics & Information Sciences
*

*The*underlying idea is to harness

*the*optimization capabilities of quantum genetic

*algorithm*to achieve good quality solutions

*for*Max SAT

*problem*. ...

*The*proposed approach is based on quantum inspired genetic principles and

*the*well known

*exact*

*algorithm*DPLL. ...

*The*complete methods examine

*the*entire search space, they fully answer

*for*

*the*

*problem*of

*satisfiability*of

*an*instance [4, 23] . ...

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