TY - JOUR

T1 - Parameterized algorithms for the Happy Set problem

AU - Asahiro, Yuichi

AU - Eto, Hiroshi

AU - Hanaka, Tesshu

AU - Lin, Guohui

AU - Miyano, Eiji

AU - Terabaru, Ippei

N1 - Funding Information:
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, JP17K00024, JP19K21537, JP21K17707, JP21K11755, and Japan Science and Technology Agency Core Research for Evolutional Science and TechnologyJPMJR1402. The authors are grateful to the anonymous reviewers for constructive comments that improved the presentation of the paper.
Funding Information:
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 , JP17K00024 , JP19K21537 , JP21K17707 , JP21K11755 , and Japan Science and Technology Agency Core Research for Evolutional Science and Technology JPMJR1402 . The authors are grateful to the anonymous reviewers for constructive comments that improved the presentation of the paper.
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2021/12/15

Y1 - 2021/12/15

N2 - In this paper we study the parameterized complexity for the MAXIMUM HAPPY SET problem (MaxHS): 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; 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 with respect to k even if the input graph is a split graph. Then, we prove the fixed-parameter tractability of MaxHS when parameterized by tree-width, by clique-width plus k, by neighborhood diversity, or by cluster deletion number.

AB - In this paper we study the parameterized complexity for the MAXIMUM HAPPY SET problem (MaxHS): 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; 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 with respect to k even if the input graph is a split graph. Then, we prove the fixed-parameter tractability of MaxHS when parameterized by tree-width, by clique-width plus k, by neighborhood diversity, or by cluster deletion number.

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U2 - 10.1016/j.dam.2021.07.005

DO - 10.1016/j.dam.2021.07.005

M3 - Article

AN - SCOPUS:85111074192

VL - 304

SP - 32

EP - 44

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -