Parameterized algorithms for the Happy Set problem

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

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)32-44
Number of pages13
JournalDiscrete Applied Mathematics
Publication statusPublished - Dec 15 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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