TY - GEN

T1 - Graph Classes and Approximability of the Happy Set Problem

AU - Asahiro, Yuichi

AU - Eto, Hiroshi

AU - Hanaka, Tesshu

AU - Lin, Guohui

AU - Miyano, Eiji

AU - Terabaru, Ippei

N1 - Funding Information:
Acknowledgments. We would like to thank the anonymous referees for their helpful comments, especially pointing out small errors in the proof of Theorem 4. This work was partially supported by the Natural Sciences and Engineering Research Council of Canada, the Grants-in-Aid for Scientific Research of Japan (KAKENHI) Grant Numbers JP17K00016 and JP17K00024, JP19K21537, and JST CREST JPMJR1402.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-030-58150-3_27

DO - 10.1007/978-3-030-58150-3_27

M3 - Conference contribution

AN - SCOPUS:85091112536

SN - 9783030581497

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 335

EP - 346

BT - Computing and Combinatorics - 26th International Conference, COCOON 2020, Proceedings

A2 - Kim, Donghyun

A2 - Uma, R.N.

A2 - Cai, Zhipeng

A2 - Lee, Dong Hoon

PB - Springer Science and Business Media Deutschland GmbH

T2 - 26th International Conference on Computing and Combinatorics, COCOON 2020

Y2 - 29 August 2020 through 31 August 2020

ER -