Parameterized algorithms for constraint satisfaction problems above average with global cardinality constraints

Xue Chen, Yuan Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a constraint satisfaction problem (CSP) on n variables, x1; x2; : : : ; xn 2 ( ±1), andmconstraints, a global cardinality constraint has the form of Pn i=1 xi = (1 2p)n, where p ∈ ((1); 1 (1)) and pn is an integer. Let AV G be the expected number of constraints satisfied by randomly choosing an assignment to x1; x2; : : : ; xn, complying with the global cardinality constraint. The CSP above average with the global cardinality constraint problem asks whether there is an assignment (complying with the cardinality constraint) that satisfies more than (AV G + t) constraints, where t is an input parameter. In this paper, we present an algorithm that finds a valid assignment satisfying more than (AV G + t) constraints (if there exists one) in time (2O(t2) + nO(d)). Therefore, the CSP above average with the global cardinality constraint problem is fixed-parameter tractable.

Original languageEnglish (US)
Title of host publication28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
EditorsPhilip N. Klein
PublisherAssociation for Computing Machinery,
Pages358-377
Number of pages20
ISBN (Electronic)9781611974782
StatePublished - Jan 1 2017
Externally publishedYes
Event28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain
Duration: Jan 16 2017Jan 19 2017

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
CountrySpain
CityBarcelona
Period1/16/171/19/17

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ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Chen, X., & Zhou, Y. (2017). Parameterized algorithms for constraint satisfaction problems above average with global cardinality constraints. In P. N. Klein (Ed.), 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 (pp. 358-377). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery,.