Independent dominating set problem revisited

Ching Hao Liu, Sheung Hung Poon, Jin Yong Lin

Research output: Journal PublicationArticlepeer-review

9 Citations (Scopus)

Abstract

An independent dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one vertex of D and no two vertices in D are adjacent. The independent dominating set (IDS) problem asks for an independent dominating set with minimum cardinality. First, we show that the independent dominating set problem and the dominating set problem on cubic bipartite graphs are both NP-complete. As an additional result, we give an alternative and more direct proof for the NP-completeness of both the independent dominating set problem and the dominating set problem on at-most-cubic grid graphs. Next, we show that there are fixed-parameter tractable algorithms for the independent dominating set problem and the dominating set problem on at-most-cubic graphs, which run in O(3.3028k+n) and O(4.2361k+n) time, respectively. Moreover, we consider the weighted independent dominating set problem on (k, ℓ)-graphs. We show that the problem on (2, 1)-graphs is NP-complete. We also show that the problem can be solved in linear time for (1, 1)-graphs and in polynomial time for (1, ℓ)-graphs for constant ℓ, respectively.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalTheoretical Computer Science
Volume562
Issue numberC
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • (k, ℓ)-graph
  • At-most-cubic grid graph
  • Cubic bipartite graph
  • Dominating set
  • FPT-algorithm
  • Independent dominating set
  • NP-complete
  • Weighted independent dominating set

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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