Graph Classes and Approximability of the Happy Set Problem

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper we study the approximability of the Maximum Happy Set problem (MaxHS) and the computational complexity of MaxHS on graph classes: For an undirected graph and a subset of vertices, a vertex v is happy if v and all its neighbors are in S; otherwise unhappy. Given an undirected graph and an integer k, the goal of MaxHS is to find a subset of k vertices such that the number of happy vertices is maximized. MaxHS is known to be NP-hard. In this paper, we design a-approximation algorithm for MaxHS on graphs with maximum degree. Next, we show that the approximation ratio can be improved to if the input is a connected graph and its maximum degree is a constant. Then, we show that MaxHS can be solved in polynomial time if the input graph is restricted to proper interval graphs, or block graphs. We prove nevertheless that MaxHS remains NP-hard even for bipartite graphs or for cubic graphs.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 26th International Conference, COCOON 2020, Proceedings
EditorsDonghyun Kim, R.N. Uma, Zhipeng Cai, Dong Hoon Lee
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783030581497
Publication statusPublished - 2020
Event26th International Conference on Computing and Combinatorics, COCOON 2020 - Atlanta, United States
Duration: Aug 29 2020Aug 31 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12273 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference26th International Conference on Computing and Combinatorics, COCOON 2020
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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