Parameterized algorithms for the Happy Set problem

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 Max...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 304; pp. 32 - 44
Main Authors: Asahiro, Yuichi, Eto, Hiroshi, Hanaka, Tesshu, Lin, Guohui, Miyano, Eiji, Terabaru, Ippei
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.12.2021
Elsevier BV
Subjects:
Algorithms
Apexes
Fixed-parameter tractability
Graph parameters
Maximum happy set problem
Parameterization
Parameterized complexity
Maximum happy set problem
Graph parameters
Fixed-parameter tractability
Parameterized complexity
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary: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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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2021.07.005