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Structure in locally optimal solutions

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M. W. KrentelAuthors Info & Claims

SFCS '89: Proceedings of the 30th Annual Symposium on Foundations of Computer Science

Pages 216 - 221

https://doi.org/10.1109/SFCS.1989.63481

Published: 30 October 1989 Publication History

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Abstract

A class of local search problems, PLS (polynomial-time local search), as defined by D.S. Johnson et al. (see J. Comput. Syst. Sci., vol.37, no.1, p.79-100 (1988)) is considered. PLS captures much of the structure of NP problems at the level of their feasible solutions and neighborhoods. It is first shown that CNF (conjunctive normal form) satisfiability is PLS-complete, even with simultaneously bounded size clauses and bounded number of occurrences of variables. This result is used to show that traveling salesman under the k-opt neighborhood is also PLS-complete. It is argued that PLS-completeness is the normal behavior of NP-complete problems.

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Göös MHollender AJain SMaystre GPires WRobere RTao R(2024)Separations in Proof Complexity and TFNPJournal of the ACM10.1145/366375871:4(1-45)Online publication date: 9-May-2024
https://dl.acm.org/doi/10.1145/3663758
Hollender A(2022)The classes PPA-kTheoretical Computer Science10.1016/j.tcs.2021.06.016885:C(15-29)Online publication date: 22-Apr-2022
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Caragiannis IFanelli AGravin N(2017)Short Sequences of Improvement Moves Lead to Approximate Equilibria in Constraint Satisfaction GamesAlgorithmica10.1007/s00453-016-0143-x77:4(1143-1158)Online publication date: 1-Apr-2017
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Structure in locally optimal solutions
1. Mathematics of computing
2. Theory of computation
  1. Computational complexity and cryptography
  2. Design and analysis of algorithms

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SFCS '89: Proceedings of the 30th Annual Symposium on Foundations of Computer Science

October 1989

586 pages

ISBN:0818619821

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IEEE Computer Society

United States

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Published: 30 October 1989

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Göös MHollender AJain SMaystre GPires WRobere RTao R(2024)Separations in Proof Complexity and TFNPJournal of the ACM10.1145/366375871:4(1-45)Online publication date: 9-May-2024
https://dl.acm.org/doi/10.1145/3663758
Hollender A(2022)The classes PPA-kTheoretical Computer Science10.1016/j.tcs.2021.06.016885:C(15-29)Online publication date: 22-Apr-2022
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Hansen KIbsen-Jensen RPodolskii VTsigaridas E(2013)Patience of matrix gamesDiscrete Applied Mathematics10.1016/j.dam.2013.05.008161:16-17(2440-2459)Online publication date: 1-Nov-2013
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Elsässer RTscheuschner T(2011)Settling the complexity of local max-cut (almost) completelyProceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I10.5555/2027127.2027146(171-182)Online publication date: 4-Jul-2011
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Monien BTscheuschner T(2010)On the power of nodes of degree four in the local max-cut problemProceedings of the 7th international conference on Algorithms and Complexity10.1007/978-3-642-13073-1_24(264-275)Online publication date: 26-May-2010
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Angel E(2005)A survey of approximation results for local search algorithmsEfficient Approximation and Online Algorithms10.5555/2168139.2168142(30-73)Online publication date: 1-Jan-2005
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