1. Parameterized algorithms for the Happy Set problem.
- Author
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Asahiro, Yuichi, Eto, Hiroshi, Hanaka, Tesshu, Lin, Guohui, Miyano, Eiji, and Terabaru, Ippei
- Subjects
- *
ALGORITHMS , *UNDIRECTED graphs , *INTEGERS - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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