Distributed Independent Sets in Interval and Segment Intersection Graphs

Barun Gorain, Kaushik Mondal, Supantha Pandit

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

1 Scopus citations

Abstract

The Maximal Independent Set problem is a well-studied problem in the distributed community. We study Maximum and Maximal Independent Set problems on two geometric intersection graphs; interval graphs and axis-parallel segment intersection graphs, and present deterministic distributed algorithms in the local communication model. We compute the maximum independent set on interval graphs in O(k) rounds and O(n) messages, where k is the size of the maximum independent set and n is the number of nodes in the graph. We provide a matching lower bound of Ω(k) on the number of rounds whereas Ω(n) is a trivial lower bound on message complexity. Thus our algorithm is both time and message optimal. We also study the maximal independent set problem in bi-interval graphs, a special case of the interval graphs where the intervals have two different lengths. We prove that a maximal independent set can be computed in bi-interval graphs in constant rounds that is 16 -approximation. For axis-parallel segment intersection graphs, we design an algorithm that finds a maximal independent set in O(D) rounds, where D is the diameter of the graph. We further show that this independent set is a 12 -approximation. The results in this paper extend the results of Molla et al. [J. Parallel Distrib. Comput. 2019].

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
Pages175-188
Number of pages14
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

Keywords

  • Approximation algorithm
  • Distributed algorithm
  • Interval graph
  • Maximal Independent Set
  • Segment intersection graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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