Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond

Dibyayan Chakraborty, Antoine Dailly, Sandip Das, Florent Foucaud, Harmender Gahlawat, Subir Kumar Ghosh

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

6 Scopus citations

Abstract

A path is isometric if it is a shortest path between its endpoints. In this article, we consider the graph covering problem Isometric Path Cover, where we want to cover all the vertices of the graph using a minimum-size set of isometric paths. Although this problem has been considered from a structural point of view (in particular, regarding applications to pursuit-evasion games), it is little studied from the algorithmic perspective. We consider Isometric Path Cover on chordal graphs, and show that the problem is NP-hard for this class. On the positive side, for chordal graphs, we design a 4-approximation algorithm and an FPT algorithm for the parameter solution size. The approximation algorithm is based on a reduction to the classic path covering problem on a suitable directed acyclic graph obtained from a breadth first search traversal of the graph. The approximation ratio of our algorithm is 3 for interval graphs and 2 for proper interval graphs. Moreover, we extend the analysis of our approximation algorithm to k-chordal graphs (graphs whose induced cycles have length at most k) by showing that it has an approximation ratio of k + 7 for such graphs, and to graphs of treelength at most ℓ, where the approximation ratio is at most 6ℓ + 2.

Original languageEnglish
Title of host publication33rd International Symposium on Algorithms and Computation, ISAAC 2022
EditorsSang Won Bae, Heejin Park
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772587
DOIs
StatePublished - 1 Dec 2022
Event33rd International Symposium on Algorithms and Computation, ISAAC 2022 - Virtual, Online, Korea, Republic of
Duration: 19 Dec 202221 Dec 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume248
ISSN (Print)1868-8969

Conference

Conference33rd International Symposium on Algorithms and Computation, ISAAC 2022
Country/TerritoryKorea, Republic of
CityVirtual, Online
Period19/12/2221/12/22

Keywords

  • Approximation algorithm
  • AT-free graph
  • Chordal graph
  • Chordality
  • FPT algorithm
  • Interval graph
  • Isometric path cover
  • Shortest paths
  • Treelength
  • Treewidth

ASJC Scopus subject areas

  • Software

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