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An Improved Exact Algorithm for the Exact Satisfiability Problem
[article]
2020
arXiv
pre-print
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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]
2003
Lecture Notes in Computer Science
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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
2011
Algorithmica
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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]
2010
arXiv
pre-print
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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]
2006
arXiv
pre-print
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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
2013
52nd IEEE Conference on Decision and Control
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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
2014
IEEE Transactions on Power Systems
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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
2020
Journal of Advances in Mathematics and Computer Science
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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]
2019
arXiv
pre-print
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2019 pre-print arXiv:1905.06503v1 fatcat:tgi5exgbmrgrxbmk4q43guxaym
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
2014
Theoretical Computer Science
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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]
2014
arXiv
pre-print
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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]
2005
Lecture Notes in Computer Science
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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
2006
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
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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
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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
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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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