Parameterized Complexity of Minimum Membership Dominating Set

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

doi:10.1007/978-3-030-96731-4_24

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 proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

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 language	English
Title of host publication	WALCOM
Subtitle of host publication	Algorithms and Computation - 16th International Conference and Workshops, WALCOM 2022, Proceedings
Editors	Petra Mutzel, Md. Saidur Rahman, Slamin
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	288-299
Number of pages	12
ISBN (Print)	9783030967307
DOIs	https://doi.org/10.1007/978-3-030-96731-4_24
State	Published - 1 Jan 2022
Externally published	Yes
Event	16th International Conference and Workshops on Algorithms and Computation, WALCOM 2022 - Jember, Indonesia Duration: 24 Mar 2022 → 26 Mar 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13174 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Conference and Workshops on Algorithms and Computation, WALCOM 2022
Country/Territory	Indonesia
City	Jember
Period	24/03/22 → 26/03/22

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/978-3-030-96731-4_24

Cite this

Agrawal, A., Choudhary, P., Narayanaswamy, N. S., Nisha, K. K., & Ramamoorthi, V. (2022). Parameterized Complexity of Minimum Membership Dominating Set. In P. Mutzel, M. S. Rahman, & Slamin (Eds.), WALCOM: Algorithms and Computation - 16th International Conference and Workshops, WALCOM 2022, Proceedings (pp. 288-299). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13174 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-96731-4_24

Agrawal, Akanksha ; Choudhary, Pratibha ; Narayanaswamy, N. S. et al. / Parameterized Complexity of Minimum Membership Dominating Set. WALCOM: Algorithms and Computation - 16th International Conference and Workshops, WALCOM 2022, Proceedings. editor / Petra Mutzel ; Md. Saidur Rahman ; Slamin. Springer Science and Business Media Deutschland GmbH, 2022. pp. 288-299 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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.",

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Agrawal, A, Choudhary, P, Narayanaswamy, NS, Nisha, KK & Ramamoorthi, V 2022, Parameterized Complexity of Minimum Membership Dominating Set. in P Mutzel, MS Rahman & Slamin (eds), WALCOM: Algorithms and Computation - 16th International Conference and Workshops, WALCOM 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13174 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 288-299, 16th International Conference and Workshops on Algorithms and Computation, WALCOM 2022, Jember, Indonesia, 24/03/22. https://doi.org/10.1007/978-3-030-96731-4_24

Parameterized Complexity of Minimum Membership Dominating Set. / Agrawal, Akanksha; Choudhary, Pratibha; Narayanaswamy, N. S. et al.
WALCOM: Algorithms and Computation - 16th International Conference and Workshops, WALCOM 2022, Proceedings. ed. / Petra Mutzel; Md. Saidur Rahman; Slamin. Springer Science and Business Media Deutschland GmbH, 2022. p. 288-299 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13174 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Agrawal A, Choudhary P, Narayanaswamy NS, Nisha KK, Ramamoorthi V. Parameterized Complexity of Minimum Membership Dominating Set. In Mutzel P, Rahman MS, Slamin, editors, WALCOM: Algorithms and Computation - 16th International Conference and Workshops, WALCOM 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 288-299. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-96731-4_24