TY - GEN

T1 - Parameterized Complexity of Safe Set

AU - Belmonte, Rémy

AU - Hanaka, Tesshu

AU - Katsikarelis, Ioannis

AU - Lampis, Michael

AU - Ono, Hirotaka

AU - Otachi, Yota

N1 - Funding Information:
Partially supported by JSPS and MAEDI under the Japan-France Integrated Action Program (SAKURA) Project GRAPA 38593YJ, and by JSPS/MEXT KAKENHI Grant Numbers JP24106004, JP17H01698, JP18K11157, JP18K11168, JP18K11169, JP18H04091, 18H06469.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85066895249&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066895249&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-17402-6_4

DO - 10.1007/978-3-030-17402-6_4

M3 - Conference contribution

AN - SCOPUS:85066895249

SN - 9783030174019

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

SP - 38

EP - 49

BT - Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings

A2 - Heggernes, Pinar

PB - Springer Verlag

T2 - 11th International Conference on Algorithms and Complexity, CIAC 2019

Y2 - 27 May 2019 through 29 May 2019

ER -