### Abstract

In this paper we introduce the Maximum Happy Set problem (MaxHS) and study its parameterized complexity: 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; and 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 when parameterized by k. Then, we prove the fixed-parameter tractability of MaxHS when parameterized by the tree-width, the clique-width and k, the neighborhood diversity, or the twin-cover number.

Original language | English |
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Title of host publication | WALCOM |

Subtitle of host publication | Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings |

Editors | M. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung |

Publisher | Springer |

Pages | 323-328 |

Number of pages | 6 |

ISBN (Print) | 9783030398804 |

DOIs | |

Publication status | Published - Jan 1 2020 |

Event | 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore Duration: Mar 31 2020 → Apr 2 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12049 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 |
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Country | Singapore |

City | Singapore |

Period | 3/31/20 → 4/2/20 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings*(pp. 323-328). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12049 LNCS). Springer. https://doi.org/10.1007/978-3-030-39881-1_27