Parameterized algorithms for maximum cut with connectivity constraints

Hiroshi Eto, Tesshu Hanaka, Yasuaki Kobayashi, Yusuke Kobayashi

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

Abstract

We study two variants of Maximum Cut, which we call Connected Maximum Cut and Maximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NP-complete even on planar graphs whereas Maximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size.

Original languageEnglish
Title of host publication14th International Symposium on Parameterized and Exact Computation, IPEC 2019
EditorsBart M. P. Jansen, Jan Arne Telle
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771290
DOIs
Publication statusPublished - Dec 2019
Event14th International Symposium on Parameterized and Exact Computation, IPEC 2019 - Munich, Germany
Duration: Sep 11 2019Sep 13 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume148
ISSN (Print)1868-8969

Conference

Conference14th International Symposium on Parameterized and Exact Computation, IPEC 2019
CountryGermany
CityMunich
Period9/11/199/13/19

Fingerprint

Computational complexity
Polynomials

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Eto, H., Hanaka, T., Kobayashi, Y., & Kobayashi, Y. (2019). Parameterized algorithms for maximum cut with connectivity constraints. In B. M. P. Jansen, & J. A. Telle (Eds.), 14th International Symposium on Parameterized and Exact Computation, IPEC 2019 [13] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 148). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.IPEC.2019.13

Parameterized algorithms for maximum cut with connectivity constraints. / Eto, Hiroshi; Hanaka, Tesshu; Kobayashi, Yasuaki; Kobayashi, Yusuke.

14th International Symposium on Parameterized and Exact Computation, IPEC 2019. ed. / Bart M. P. Jansen; Jan Arne Telle. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 13 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 148).

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

Eto, H, Hanaka, T, Kobayashi, Y & Kobayashi, Y 2019, Parameterized algorithms for maximum cut with connectivity constraints. in BMP Jansen & JA Telle (eds), 14th International Symposium on Parameterized and Exact Computation, IPEC 2019., 13, Leibniz International Proceedings in Informatics, LIPIcs, vol. 148, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 14th International Symposium on Parameterized and Exact Computation, IPEC 2019, Munich, Germany, 9/11/19. https://doi.org/10.4230/LIPIcs.IPEC.2019.13
Eto H, Hanaka T, Kobayashi Y, Kobayashi Y. Parameterized algorithms for maximum cut with connectivity constraints. In Jansen BMP, Telle JA, editors, 14th International Symposium on Parameterized and Exact Computation, IPEC 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. 13. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.IPEC.2019.13
Eto, Hiroshi ; Hanaka, Tesshu ; Kobayashi, Yasuaki ; Kobayashi, Yusuke. / Parameterized algorithms for maximum cut with connectivity constraints. 14th International Symposium on Parameterized and Exact Computation, IPEC 2019. editor / Bart M. P. Jansen ; Jan Arne Telle. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. (Leibniz International Proceedings in Informatics, LIPIcs).
@inproceedings{1540d22a88cd4ecfbff7daeecb9917ac,
title = "Parameterized algorithms for maximum cut with connectivity constraints",
abstract = "We study two variants of Maximum Cut, which we call Connected Maximum Cut and Maximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NP-complete even on planar graphs whereas Maximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size.",
author = "Hiroshi Eto and Tesshu Hanaka and Yasuaki Kobayashi and Yusuke Kobayashi",
year = "2019",
month = "12",
doi = "10.4230/LIPIcs.IPEC.2019.13",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Jansen, {Bart M. P.} and Telle, {Jan Arne}",
booktitle = "14th International Symposium on Parameterized and Exact Computation, IPEC 2019",

}

TY - GEN

T1 - Parameterized algorithms for maximum cut with connectivity constraints

AU - Eto, Hiroshi

AU - Hanaka, Tesshu

AU - Kobayashi, Yasuaki

AU - Kobayashi, Yusuke

PY - 2019/12

Y1 - 2019/12

N2 - We study two variants of Maximum Cut, which we call Connected Maximum Cut and Maximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NP-complete even on planar graphs whereas Maximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size.

AB - We study two variants of Maximum Cut, which we call Connected Maximum Cut and Maximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NP-complete even on planar graphs whereas Maximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size.

UR - http://www.scopus.com/inward/record.url?scp=85077468897&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85077468897&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.IPEC.2019.13

DO - 10.4230/LIPIcs.IPEC.2019.13

M3 - Conference contribution

AN - SCOPUS:85077468897

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 14th International Symposium on Parameterized and Exact Computation, IPEC 2019

A2 - Jansen, Bart M. P.

A2 - Telle, Jan Arne

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -