Complexity and Algorithms for Semipaired Domination in Graphs

Michael A. Henning, Arti Pandey, Vikash Tripathi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

For a graph G = (V, E) with no isolated vertices, a set D⊆ V is called a semipaired dominating set of G if (i)D is a dominating set of G, and (ii)D can be partitioned into two element subsets such that the vertices in each two element set are at distance at most two. The minimum cardinality of a semipaired dominating set of G is called the semipaired domination number of G, and is denoted by γpr2(G). The Minimum Semipaired Domination problem is to find a semipaired dominating set of G of cardinality γpr2(G). In this paper, we initiate the algorithmic study of the Minimum Semipaired Domination problem. We show that the decision version of the Minimum Semipaired Domination problem is NP-complete for bipartite graphs and chordal graphs. On the positive side, we present a linear-time algorithm to compute a minimum cardinality semipaired dominating set of interval graphs. We also propose a 1 + ln (2 Δ + 2) -approximation algorithm for the Minimum Semipaired Domination problem, where Δ denotes the maximum degree of the graph and show that the Minimum Semipaired Domination problem cannot be approximated within (1 − ϵ) ln | V| for any ϵ > 0 unless P=NP.

Original languageEnglish
Pages (from-to)1225-1241
Number of pages17
JournalTheory of Computing Systems
Volume64
Issue number7
DOIs
Publication statusPublished - Oct 2020

Keywords

  • Approximation algorithm
  • Domination
  • Graph algorithm
  • Interval graphs
  • NP-complete
  • Semipaired domination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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