TY - GEN

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:
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.

PY - 2020

Y1 - 2020

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.

AB - 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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U2 - 10.1007/978-3-030-39881-1_27

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

M3 - Conference contribution

AN - SCOPUS:85080915754

SN - 9783030398804

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 323

EP - 328

BT - WALCOM

A2 - Rahman, M. Sohel

A2 - Sadakane, Kunihiko

A2 - Sung, Wing-Kin

PB - Springer

T2 - 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020

Y2 - 31 March 2020 through 2 April 2020

ER -