Hardness and Approximation for the Geodetic Set Problem in Some Graph Classes

Dibyayan Chakraborty, Florent Foucaud, Harmender Gahlawat, Subir Kumar Ghosh, Bodhayan Roy

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

6 Scopus citations

Abstract

In this paper, we study the computational complexity of finding the geodetic number of graphs. A set of vertices S of a graph G is a geodetic set if any vertex of G lies in some shortest path between some pair of vertices from S. The Minimum Geodetic Set (MGS) problem is to find a geodetic set with minimum cardinality. In this paper, we prove that solving MGS is NP-hard on planar graphs with a maximum degree six and line graphs. We also show that unless there is no polynomial time algorithm to solve MGS with sublogarithmic approximation factor (in terms of the number of vertices) even on graphs with diameter 2. On the positive side, we give an 3 \of {n}\log n\right) -approximation algorithm for MGS on general graphs of order n. We also give a 3-approximation algorithm for MGS on solid grid graphs which are planar.

Original languageEnglish
Title of host publicationAlgorithms and Discrete Applied Mathematics - 6th International Conference, CALDAM 2020, Proceedings
EditorsManoj Changat, Sandip Das
PublisherSpringer
Pages102-115
Number of pages14
ISBN (Print)9783030392185
DOIs
StatePublished - 1 Jan 2020
Externally publishedYes
Event6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020 - Hyderabad, India
Duration: 13 Feb 202015 Feb 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12016 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020
Country/TerritoryIndia
CityHyderabad
Period13/02/2015/02/20

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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