Neighborhood Persistency of the Linear Optimization Relaxation of Integer Linear Optimization

Kei Kimura, Kotaro Nakayama

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

Abstract

For an integer linear optimization (ILO) problem, persistency of its linear optimization (LO) relaxation is a property that for every optimal solution of the relaxation that assigns integer values to some variables, there exists an optimal solution of the ILO problem in which these variables retain the same values. Although persistency has been used to develop heuristic, approximation, and fixed-parameter algorithms for special cases of ILO, its applicability remains unknown in the literature. In this paper, we propose a stronger property called neighborhood persistency and show that the LO relaxation of ILO on unit-two-variable-per-inequality (UTVPI) systems is a maximal class of ILO such that its LO relaxation has (neighborhood) persistency. Our result on neighborhood persistency generalizes the previous results of Nemhauser and Trotter, Hochbaum et al., and Fiorini et al., and implies fixed-parameter tractability and two-approximability for ILO on UTVPI systems where the objective function and the variables are non-negative.

Original languageEnglish
Title of host publicationCombinatorial Optimization - 7th International Symposium, ISCO 2022, Revised Selected Papers
EditorsIvana Ljubić, Francisco Barahona, Santanu S. Dey, A. Ridha Mahjoub
PublisherSpringer Science and Business Media Deutschland GmbH
Pages312-323
Number of pages12
ISBN (Print)9783031185298
DOIs
Publication statusPublished - 2022
Event7th International Symposium on Combinatorial Optimization, ISCO 2022 - Virtual, Online
Duration: May 18 2022May 20 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13526 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Symposium on Combinatorial Optimization, ISCO 2022
CityVirtual, Online
Period5/18/225/20/22

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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