Parameterized algorithms for maximum cut with connectivity constraints

Hiroshi Eto; Tesshu Hanaka; Yasuaki Kobayashi; Yusuke Kobayashi

doi:10.4230/LIPIcs.IPEC.2019.13

Parameterized algorithms for maximum cut with connectivity constraints

Hiroshi Eto, Tesshu Hanaka, Yasuaki Kobayashi, Yusuke Kobayashi

Fields in Economic Systems

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

2 Citations (Scopus)

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 language	English
Title of host publication	14th International Symposium on Parameterized and Exact Computation, IPEC 2019
Editors	Bart M. P. Jansen, Jan Arne Telle
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771290
DOIs	https://doi.org/10.4230/LIPIcs.IPEC.2019.13
Publication status	Published - Dec 2019
Event	14th International Symposium on Parameterized and Exact Computation, IPEC 2019 - Munich, Germany Duration: Sep 11 2019 → Sep 13 2019

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	148
ISSN (Print)	1868-8969

Conference

Conference	14th International Symposium on Parameterized and Exact Computation, IPEC 2019
Country	Germany
City	Munich
Period	9/11/19 → 9/13/19

All Science Journal Classification (ASJC) codes

Software

Access to Document

10.4230/LIPIcs.IPEC.2019.13

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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 proceeding › Conference 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).

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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.",

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