Decremental Optimization of Dominating Sets Under the Reconfiguration Framework

Alexandre Blanché, Haruka Mizuta, Paul Ouvrard, Akira Suzuki

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

Abstract

Given a dominating set, how much smaller a dominating set can we find through elementary operations? Here, we proceed by iterative vertex addition and removal while maintaining the property that the set forms a dominating set of bounded size. This can be seen as the optimization variant of the dominating set reconfiguration problem, where two dominating sets are given and the question is merely whether they can be reached from one another through elementary operations. We show that this problem is PSPACE-complete, even if the input graph is a bipartite graph, a split graph, or has bounded pathwidth. On the positive side, we give linear-time algorithms for cographs, trees and interval graphs. We also study the parameterized complexity of this problem. More precisely, we show that the problem is W[2]-hard when parameterized by the upper bound on the size of an intermediary dominating set. On the other hand, we give fixed-parameter algorithms with respect to the minimum size of a vertex cover, or d + s where d is the degeneracy and s is the upper bound of the output solution.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings
EditorsLeszek Gasieniec, Leszek Gasieniec, Ralf Klasing, Tomasz Radzik
PublisherSpringer
Pages69-82
Number of pages14
ISBN (Print)9783030489656
DOIs
Publication statusPublished - 2020
Event31st International Workshop on Combinatorial Algorithms, IWOCA 2020 - Bordeaux, France
Duration: 2020 Jun 82020 Jun 10

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12126 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference31st International Workshop on Combinatorial Algorithms, IWOCA 2020
CountryFrance
CityBordeaux
Period20/6/820/6/10

Keywords

  • Combinatorial reconfiguration
  • Dominating set
  • Parameterized complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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