Computing maximum independent set on outerstring graphs and their relatives

Prosenjit Bose, Paz Carmi, Mark J. Keil, Anil Maheshwari, Saeed Mehrabi, Debajyoti Mondal, Michiel Smid

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

3 Scopus citations


A graph G with n vertices is called an outerstring graph if it has an intersection representation of a set of n curves inside a disk such that one endpoint of every curve is attached to the boundary of the disk. Given an outerstring graph representation, the Maximum Independent Set (MIS) problem of the underlying graph can be solved in O(s3) time, where s is the number of segments in the representation (Keil et al., Comput. Geom., 60:19–25, 2017). If the strings are of constant size (e.g., line segments, L -shapes, etc.), then the algorithm takes O(n3) time. In this paper, we examine the fine-grained complexity of the MIS problem on some well-known outerstring representations. We show that solving the MIS problem on grounded segment and grounded square- L representations is at least as hard as solving MIS on circle graph representations. Note that no O(n2-δ) -time algorithm, δ> 0, is known for the MIS problem on circle graphs. For the grounded string representations where the strings are y-monotone simple polygonal paths of constant length with segments at integral coordinates, we solve MIS in O(n2) time and show this to be the best possible under the strong exponential time hypothesis (SETH). For the intersection graph of n L -shapes in the plane, we give a (4 · log OPT) -approximation algorithm for MIS (where OPT denotes the size of an optimal solution), improving the previously best-known (4 · log n) -approximation algorithm of Biedl and Derka (WADS 2017).

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings
EditorsZachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783030247652
StatePublished - 1 Jan 2019
Event16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, Canada
Duration: 5 Aug 20197 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11646 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Symposium on Algorithms and Data Structures, WADS 2019

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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