Parameterized Complexity of Safe Set

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

doi:10.1007/978-3-030-17402-6_4

Parameterized Complexity of Safe Set

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Citations (Scopus)

Abstract

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 language	English
Title of host publication	Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings
Editors	Pinar Heggernes
Publisher	Springer Verlag
Pages	38-49
Number of pages	12
ISBN (Print)	9783030174019
DOIs	https://doi.org/10.1007/978-3-030-17402-6_4
Publication status	Published - 2019
Externally published	Yes
Event	11th International Conference on Algorithms and Complexity, CIAC 2019 - Rome, Italy Duration: May 27 2019 → May 29 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11485 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Conference on Algorithms and Complexity, CIAC 2019
Country/Territory	Italy
City	Rome
Period	5/27/19 → 5/29/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

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

Cite this

Belmonte, R., Hanaka, T., Katsikarelis, I., Lampis, M., Ono, H., & Otachi, Y. (2019). Parameterized Complexity of Safe Set. In P. Heggernes (Ed.), Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings (pp. 38-49). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11485 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-17402-6_4

Parameterized Complexity of Safe Set. / Belmonte, Rémy; Hanaka, Tesshu; Katsikarelis, Ioannis et al.

Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings. ed. / Pinar Heggernes. Springer Verlag, 2019. p. 38-49 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11485 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Belmonte, R, Hanaka, T, Katsikarelis, I, Lampis, M, Ono, H & Otachi, Y 2019, Parameterized Complexity of Safe Set. in P Heggernes (ed.), Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11485 LNCS, Springer Verlag, pp. 38-49, 11th International Conference on Algorithms and Complexity, CIAC 2019, Rome, Italy, 5/27/19. https://doi.org/10.1007/978-3-030-17402-6_4

Belmonte R, Hanaka T, Katsikarelis I, Lampis M, Ono H, Otachi Y. Parameterized Complexity of Safe Set. In Heggernes P, editor, Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings. Springer Verlag. 2019. p. 38-49. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-17402-6_4

Belmonte, Rémy ; Hanaka, Tesshu ; Katsikarelis, Ioannis et al. / Parameterized Complexity of Safe Set. Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings. editor / Pinar Heggernes. Springer Verlag, 2019. pp. 38-49 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{d04300af47874b7ebf9d820173f30726,

title = "Parameterized Complexity of Safe Set",

abstract = "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.",

author = "R{\'e}my Belmonte and Tesshu Hanaka and Ioannis Katsikarelis and Michael Lampis and Hirotaka Ono and Yota Otachi",

note = "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: {\textcopyright} 2019, Springer Nature Switzerland AG.; 11th International Conference on Algorithms and Complexity, CIAC 2019 ; Conference date: 27-05-2019 Through 29-05-2019",

year = "2019",

doi = "10.1007/978-3-030-17402-6_4",

language = "English",

isbn = "9783030174019",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "38--49",

editor = "Pinar Heggernes",

booktitle = "Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings",

address = "Germany",

}

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 -

Parameterized Complexity of Safe Set

Abstract

Publication series

Conference

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this