Parameterized Complexity of Minimum Membership Dominating Set

Akanksha Agrawal, Pratibha Choudhary, N. S. Narayanaswamy, K. K. Nisha, Vijayaragunathan Ramamoorthi

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

1 Scopus citations


Given a graph G= (V, E) and an integer k, the Minimum Membership Dominating Set (MMDS) problem seeks to find a dominating set S⊆ V of G such that for each v∈ V, | N[ v] ∩ S| is at most k. We investigate the parameterized complexity of the problem and obtain the following results about MMDS: 1.W[1]-hardness of the problem parameterized by the pathwidth (and thus, treewidth) of the input graph.2.W[1]-hardness parameterized by k on split graphs.3.An algorithm running in time 2 O(vc)| V| O(1), where vc is the size of a minimum-sized vertex cover of the input graph.4.An ETH-based lower bound showing that the algorithm mentioned in the previous item is optimal.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 16th International Conference and Workshops, WALCOM 2022, Proceedings
EditorsPetra Mutzel, Md. Saidur Rahman, Slamin
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783030967307
StatePublished - 1 Jan 2022
Externally publishedYes
Event16th International Conference and Workshops on Algorithms and Computation, WALCOM 2022 - Jember, Indonesia
Duration: 24 Mar 202226 Mar 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13174 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Conference and Workshops on Algorithms and Computation, WALCOM 2022

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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