TY - JOUR

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. A preliminary version of this paper appeared in the proceedings of the 11th International Conference on Algorithms and Complexity (CIAC 2019), Lecture Notes in Computer Science 11485 (2019) 38–49, doi:10.1007/978-3-030-17402-6 4.
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. A preliminary version of this paper appeared in the proceedings of the 11th International Conference on Algorithms and Complexity (CIAC 2019), Lecture Notes in Computer Science 11485 (2019) 38–49, doi:10.1007/978-3-030-17402-6 4. E-mail addresses: remy.belmonte@uec.ac.jp (Rémy Belmonte) hanaka.91t@g.chuo-u.ac.jp (Tesshu Hanaka) ioannis.katsikarelis@dauphine.fr (Ioannis Katsikarelis) michail.lampis@dauphine.fr (Michael Lampis) ono@nagoya-u.jp (Hirotaka Ono) otachi@nagoya-u.jp (Yota Otachi)
Publisher Copyright:
© 2020, Brown University. All rights reserved.

PY - 2020

Y1 - 2020

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 G − S. 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 pw and cannot be solved in time no(pw) unless the ETH is false, (2) it admits no polynomial kernel parameterized by the vertex cover number vc unless PH = Σp but (3) it is fixed-parameter tractable (FPT) when parameterized by3,the neighborhood diversity nd, and (4) it can be solved in time nf(cw) for some double exponential function f where cw is the clique-width. We also present (5) a faster fixed-parameter algorithm when parameterized by the 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 G − S. 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 pw and cannot be solved in time no(pw) unless the ETH is false, (2) it admits no polynomial kernel parameterized by the vertex cover number vc unless PH = Σp but (3) it is fixed-parameter tractable (FPT) when parameterized by3,the neighborhood diversity nd, and (4) it can be solved in time nf(cw) for some double exponential function f where cw is the clique-width. We also present (5) a faster fixed-parameter algorithm when parameterized by the solution size.

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U2 - 10.7155/jgaa.00528

DO - 10.7155/jgaa.00528

M3 - Article

AN - SCOPUS:85084473330

VL - 24

SP - 215

EP - 245

JO - Journal of Graph Algorithms and Applications

JF - Journal of Graph Algorithms and Applications

SN - 1526-1719

IS - 3

ER -