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 | |
| 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 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Software
Cite this
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
}
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 -