Incremental Optimization of Independent Sets Under the Reconfiguration Framework

Takehiro Ito, Haruka Mizuta, Naomi Nishimura, Akira Suzuki

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

3 Citations (Scopus)

Abstract

Suppose that we are given an independent set I0 of a graph G, and an integer (forumala presented). Then, we are asked to find an independent set of G having the maximum size among independent sets that are reachable from I0 by either adding or removing a single vertex at a time such that all intermediate independent sets are of size at least l. We show that this problem is PSPACE-hard even for bounded pathwidth graphs, and remains NP-hard for planar graphs. On the other hand, we give a linear-time algorithm to solve the problem for chordal graphs. We also study the parameterized complexity of the problem with respect to the following three parameters: the degeneracy d of an input graph, a lower bound l on the size of independent sets, and a lower bound s on the size of a solution reachable from I0. We show that the problem is fixed-parameter intractable when only one of d,l, and s is taken as a parameter. On the other hand, we give a fixed-parameter algorithm when parameterized by s+d this result implies that the problem parameterized only by s is fixed-parameter tractable for planar graphs, and for bounded treewidth graphs.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings
EditorsDing-Zhu Du, Zhenhua Duan, Cong Tian
PublisherSpringer Verlag
Pages313-324
Number of pages12
ISBN (Print)9783030261757
DOIs
Publication statusPublished - 2019
Event25th International Computing and Combinatorics Conference, COCOON 2019 - Xi'an, China
Duration: 2019 Jul 292019 Jul 31

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11653 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th International Computing and Combinatorics Conference, COCOON 2019
CountryChina
CityXi'an
Period19/7/2919/7/31

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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