Parameterized Complexity of Safe Set

Rémy Belmonte, Tesshu Hanaka, Ioannis Katsikarelis, Michael Lampis, Hirotaka Ono, Yota Otachi

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

3 Citations (Scopus)


In this paper we study the problem of finding a small safe set S in a graph G, i.e. a non-empty set of vertices such that no connected component of G[S] is adjacent to a larger component in. We enhance our understanding of the problem from the viewpoint of parameterized complexity by showing that (1) the problem is W[2]-hard when parameterized by the pathwidth and cannot be solved in time unless the ETH is false, (2) it admits no polynomial kernel parameterized by the vertex cover number unless, but (3) it is fixed-parameter tractable (FPT) when parameterized by the neighborhood diversity, and (4) it can be solved in time for some double exponential function f where is the clique-width. We also present (5) a faster FPT algorithm when parameterized by solution size.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings
EditorsPinar Heggernes
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783030174019
Publication statusPublished - 2019
Externally publishedYes
Event11th International Conference on Algorithms and Complexity, CIAC 2019 - Rome, Italy
Duration: May 27 2019May 29 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11485 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Conference on Algorithms and Complexity, CIAC 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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