On the Complexity of Minimum Maximal Acyclic Matchings

Juhi Chaudhary; Sounaka Mishra; B. S. Panda

doi:10.1007/978-3-031-22105-7_10

On the Complexity of Minimum Maximal Acyclic Matchings

Juhi Chaudhary, Sounaka Mishra, B. S. Panda

Department of Computer Science

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

1 Scopus citations

Abstract

Given a graph G, Min-Max-Acy-Matching is the problem of finding a maximal matching M in G of minimum cardinality such that the set of M-saturated vertices induces an acyclic subgraph in G. Min-Max-Acy-Matching is known to be NP -hard. In this paper, we strengthen this result by proving that the decision version of Min-Max-Acy-Matching is NP -complete for planar perfect elimination bipartite graphs. We also prove that Min-Max-Acy-Matching for bipartite graphs cannot be approximated within a ratio of n¹ ^- ^ϵ, for any ϵ> 0 unless P= NP. Finally, we show that Min-Max-Acy-Matching is APX -hard for 4-regular graphs.

Original language	English
Title of host publication	Computing and Combinatorics - 28th International Conference, COCOON 2022, Proceedings
Editors	Yong Zhang, Dongjing Miao, Rolf Möhring
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	106-117
Number of pages	12
ISBN (Print)	9783031221040
DOIs	https://doi.org/10.1007/978-3-031-22105-7_10
State	Published - 1 Jan 2022
Event	28th International Conference on Computing and Combinatorics, COCOON 2022 - Shenzhen, China Duration: 22 Oct 2022 → 24 Oct 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13595 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	28th International Conference on Computing and Combinatorics, COCOON 2022
Country/Territory	China
City	Shenzhen
Period	22/10/22 → 24/10/22

Keywords

APX -hardness
Acyclic matching
Matching
Minimum maximal acyclic matching
NP -completeness

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-22105-7_10

Cite this

Chaudhary, J., Mishra, S., & Panda, B. S. (2022). On the Complexity of Minimum Maximal Acyclic Matchings. In Y. Zhang, D. Miao, & R. Möhring (Eds.), Computing and Combinatorics - 28th International Conference, COCOON 2022, Proceedings (pp. 106-117). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13595 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-22105-7_10

Chaudhary, Juhi ; Mishra, Sounaka ; Panda, B. S. / On the Complexity of Minimum Maximal Acyclic Matchings. Computing and Combinatorics - 28th International Conference, COCOON 2022, Proceedings. editor / Yong Zhang ; Dongjing Miao ; Rolf Möhring. Springer Science and Business Media Deutschland GmbH, 2022. pp. 106-117 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Chaudhary, J, Mishra, S & Panda, BS 2022, On the Complexity of Minimum Maximal Acyclic Matchings. in Y Zhang, D Miao & R Möhring (eds), Computing and Combinatorics - 28th International Conference, COCOON 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13595 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 106-117, 28th International Conference on Computing and Combinatorics, COCOON 2022, Shenzhen, China, 22/10/22. https://doi.org/10.1007/978-3-031-22105-7_10

On the Complexity of Minimum Maximal Acyclic Matchings. / Chaudhary, Juhi; Mishra, Sounaka; Panda, B. S.
Computing and Combinatorics - 28th International Conference, COCOON 2022, Proceedings. ed. / Yong Zhang; Dongjing Miao; Rolf Möhring. Springer Science and Business Media Deutschland GmbH, 2022. p. 106-117 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13595 LNCS).

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

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Chaudhary J, Mishra S, Panda BS. On the Complexity of Minimum Maximal Acyclic Matchings. In Zhang Y, Miao D, Möhring R, editors, Computing and Combinatorics - 28th International Conference, COCOON 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 106-117. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-22105-7_10