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

Gordon Hoi
2020 arXiv   pre-print
Since it is 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"  ... 
arXiv:2010.03850v3 fatcat:d7mlnhplnja45kwdixmywh2zoa

Exact Algorithms for NP-Hard Problems: A Survey [chapter]

Gerhard J. Woeginger
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.  ... 
doi:10.1007/3-540-36478-1_17 fatcat:5m4p25aq65gpjnbwxsbxgrsnz4

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

Venkatesh Raman, Saket Saurabh
2011 Algorithmica  
In particular, 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).  ... 
doi:10.1007/s00453-011-9605-3 fatcat:5bwu4ykmlrcypdm5wzdvtehirq

Using CSP To Improve Deterministic 3-SAT [article]

Konstantin Kutzkov, Dominik Scheder
2010 arXiv   pre-print
This way, we 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.  ... 
arXiv:1007.1166v2 fatcat:ym467qyej5g2zh7tblo2ven2eq

An Improved Exact Algorithm for the Domatic Number Problem [article]

Tobias Riege, Jörg Rothe, Holger Spakowski, Masaki Yamamoto
2006 arXiv   pre-print
To prove our result, we combine 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.  ... 
arXiv:cs/0603060v1 fatcat:tthcokzv7fe53h4gwwasry3jky

Optimal power flow in direct current networks

Lingwen Gan, Steven H. Low
2013 52nd IEEE Conference on Decision and Control  
In this paper, we study 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.  ... 
doi:10.1109/cdc.2013.6760774 dblp:conf/cdc/GanL13 fatcat:7maq55kqazdkpklwqv7ncxwd64

Optimal Power Flow in Direct Current Networks

Lingwen Gan, Steven H. Low
2014 IEEE Transactions on Power Systems  
In this paper, we study 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.  ... 
doi:10.1109/tpwrs.2014.2313514 fatcat:y5hqnpg26rf3pj3j5ox3yhro3a

Discrete Artificial Dragonflies Algorithm in Agent Based Modelling for Exact Boolean kSatisfiability Problem

Hamza Abubakar, Sagir Abdu M., Surajo Yusuf, Yusuf Abdurrahman
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.  ... 
doi:10.9734/jamcs/2020/v35i430275 fatcat:p2bcxneetnamxca3er7rrfbnue

Parameterized Inapproximability of Exact Cover and Nearest Codeword [article]

Venkatesan Guruswami, Patrick Lin
2019 arXiv   pre-print
We prove that, assuming ETH, 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.  ... 
arXiv:1905.06503v2 fatcat:ewnbq3n4dzfjjauovlj7yv52o4

Approximating MAX SAT by moderately exponential and parameterized algorithms

Bruno Escoffier, Vangelis Th. Paschos, Emeric Tourniaire
2014 Theoretical Computer Science  
We study approximation of 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.  ... 
doi:10.1016/j.tcs.2014.10.039 fatcat:p4spt2lilzgb3kgxqwzbws3ncm

Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints [article]

Kenya Ueno
2014 arXiv   pre-print
Our 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.  ... 
arXiv:1405.6851v2 fatcat:ajyhfho7jvhe5oh5puxl6o2dcm

On the Parameterized Complexity of Exact Satisfiability Problems [chapter]

Joachim Kneis, Daniel Mölle, Stefan Richter, Peter Rossmanith
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.  ... 
doi:10.1007/11549345_49 fatcat:lnel7naotbfxze64upgfrbmiii

Confronting hardness using a hybrid approach

Virginia Vassilevska, Ryan Williams, Shan Leung Maverick Woo
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.  ... 
doi:10.1145/1109557.1109558 fatcat:4g2juiedlbgbxjodluo5v6rwo4

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

Abdesslem Layeb, Djamel-Eddine Saidouni
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] .  ... 
doi:10.12785/amis/080109 fatcat:qmyh7erwejaovbuaxp4xe4gohi
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