Balanced Independent and Dominating Sets on Colored Interval Graphs

Sujoy Bhore, Jan Henrik Haunert, Fabian Klute, Guangping Li, Martin Nöllenburg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study two new versions of independent and dominating set problems on vertex-colored interval graphs, namely f-Balanced Independent Set (f-BIS) and f-Balanced Dominating Set (f-BDS). Let G= (V, E) be an interval graph with a color assignment function γ:V→{1,…,k} that maps all vertices in G onto k colors. A subset of vertices S⊆ V is called f-balanced if S contains f vertices from each color class. In the f-BIS and f-BDS problems, the objective is to compute an independent set or a dominating set that is f-balanced. We show that both problems are NP-complete even on proper interval graphs. For the BIS problem on interval graphs, we design two FPT algorithms, one parameterized by (f, k) and the other by the vertex cover number of G. Moreover, for an optimization variant of BIS on interval graphs, we present a polynomial time approximation scheme (PTAS) and an O(nlog n) time 2-approximation algorithm.

Original languageEnglish
Title of host publicationSOFSEM 2021
Subtitle of host publicationTheory and Practice of Computer Science - 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021, Proceedings
EditorsTomáš Bureš, Riccardo Dondi, Johann Gamper, Giovanna Guerrini, Tomasz Jurdzinski, Claus Pahl, Florian Sikora, Prudence W. Wong
PublisherSpringer Science and Business Media Deutschland GmbH
Pages89-103
Number of pages15
ISBN (Print)9783030677305
DOIs
StatePublished - 1 Jan 2021
Externally publishedYes
Event47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021 - Bolzano-Bozen, Italy
Duration: 25 Jan 202129 Jan 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12607 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021
Country/TerritoryItaly
CityBolzano-Bozen
Period25/01/2129/01/21

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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