Parameterized algorithms for the happy set problem

Yuichi Asahiro; Hiroshi Eto; Tesshu Hanaka; Guohui Lin; Eiji Miyano; Ippei Terabaru

doi:10.1007/978-3-030-39881-1_27

Parameterized algorithms for the happy set problem

Yuichi Asahiro, Hiroshi Eto, Tesshu Hanaka, Guohui Lin, Eiji Miyano, Ippei Terabaru

Fields in Economic Systems

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

6 Citations (Scopus)

Abstract

In this paper we introduce the Maximum Happy Set problem (MaxHS) and study its parameterized complexity: For an undirected graph G = (V,E) and a subset S ⊆ V of vertices, a vertex v is happy if v and all its neighbors are in S; and otherwise unhappy. Given an undirected graph G = (V,E) and an integer k, the goal of MaxHS is to find a subset S ⊆ V of k vertices such that the number of happy vertices is maximized. In this paper we first show that MaxHS is W[1]-hard when parameterized by k. Then, we prove the fixed-parameter tractability of MaxHS when parameterized by the tree-width, the clique-width and k, the neighborhood diversity, or the twin-cover number.

Original language	English
Title of host publication	WALCOM
Subtitle of host publication	Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings
Editors	M. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung
Publisher	Springer
Pages	323-328
Number of pages	6
ISBN (Print)	9783030398804
DOIs	https://doi.org/10.1007/978-3-030-39881-1_27
Publication status	Published - 2020
Event	14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore Duration: Mar 31 2020 → Apr 2 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12049 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
Country/Territory	Singapore
City	Singapore
Period	3/31/20 → 4/2/20

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-39881-1_27

Cite this

Asahiro, Y., Eto, H., Hanaka, T., Lin, G., Miyano, E., & Terabaru, I. (2020). Parameterized algorithms for the happy set problem. In M. S. Rahman, K. Sadakane, & W-K. Sung (Eds.), WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings (pp. 323-328). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12049 LNCS). Springer. https://doi.org/10.1007/978-3-030-39881-1_27

Parameterized algorithms for the happy set problem. / Asahiro, Yuichi; Eto, Hiroshi; Hanaka, Tesshu et al.

WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. ed. / M. Sohel Rahman; Kunihiko Sadakane; Wing-Kin Sung. Springer, 2020. p. 323-328 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12049 LNCS).

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

Asahiro, Y, Eto, H, Hanaka, T, Lin, G, Miyano, E & Terabaru, I 2020, Parameterized algorithms for the happy set problem. in MS Rahman, K Sadakane & W-K Sung (eds), WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12049 LNCS, Springer, pp. 323-328, 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020, Singapore, Singapore, 3/31/20. https://doi.org/10.1007/978-3-030-39881-1_27

Asahiro Y, Eto H, Hanaka T, Lin G, Miyano E, Terabaru I. Parameterized algorithms for the happy set problem. In Rahman MS, Sadakane K, Sung W-K, editors, WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. Springer. 2020. p. 323-328. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-39881-1_27

Asahiro, Yuichi ; Eto, Hiroshi ; Hanaka, Tesshu et al. / Parameterized algorithms for the happy set problem. WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings. editor / M. Sohel Rahman ; Kunihiko Sadakane ; Wing-Kin Sung. Springer, 2020. pp. 323-328 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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N1 - Funding Information: Acknowledgments. This work was partially supported by the Natural Sciences and Engineering Research Council of Canada, the Grants-in-Aid for Scientific Research of Japan (KAKENHI) Grant Numbers JP17K00016 and JP17K00024, JP19K21537, and JST CREST JPMJR1402. Publisher Copyright: © Springer Nature Switzerland AG 2020.

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N2 - In this paper we introduce the Maximum Happy Set problem (MaxHS) and study its parameterized complexity: For an undirected graph G = (V,E) and a subset S ⊆ V of vertices, a vertex v is happy if v and all its neighbors are in S; and otherwise unhappy. Given an undirected graph G = (V,E) and an integer k, the goal of MaxHS is to find a subset S ⊆ V of k vertices such that the number of happy vertices is maximized. In this paper we first show that MaxHS is W[1]-hard when parameterized by k. Then, we prove the fixed-parameter tractability of MaxHS when parameterized by the tree-width, the clique-width and k, the neighborhood diversity, or the twin-cover number.

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Parameterized algorithms for the happy set problem

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