Parameterized algorithms for the Happy Set problem

被引：2

作者：

Asahiro, Yuichi ^{[1
]}

Eto, Hiroshi ^{[2
]}

Hanaka, Tesshu ^{[3
]}

Lin, Guohui ^{[4
]}

Miyano, Eiji ^{[5
]}

Terabaru, Ippei ^{[5
]}

机构：

[1] Kyushu Sangyo Univ, Fukuoka, Japan

[2] Kyushu Univ, Fukuoka, Japan

[3] Nagoya Univ, Nagoya, Aichi, Japan

[4] Univ Alberta, Edmonton, AB, Canada

[5] Kyushu Inst Technol, Iizuka, Fukuoka, Japan

来源：

DISCRETE APPLIED MATHEMATICS | 2021年 / 304卷

基金：

加拿大自然科学与工程研究理事会; 日本科学技术振兴机构;

关键词：

Maximum happy set problem; Parameterized complexity; Fixed-parameter tractability; Graph parameters; MODULAR DECOMPOSITION; CLIQUE-WIDTH; COMPLEXITY; TREEWIDTH; BOUNDS;

D O I：

10.1016/j.dam.2021.07.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 subset of V of vertices, a vertex upsilon is happy if upsilon 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 subset of 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. (C) 2021 Elsevier B.V. All rights reserved.

引用

页码：32 / 44

页数：13

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