TY - GEN
T1 - Parameterized algorithms for maximum cut with connectivity constraints
AU - Eto, Hiroshi
AU - Hanaka, Tesshu
AU - Kobayashi, Yasuaki
AU - Kobayashi, Yusuke
N1 - Funding Information:
Acknowledgements We thank Akitoshi Kawamura and Yukiko Yamauchi for giving an opportunity to discuss in the Open Problem Seminar at Kyushu University. This work is partially supported by JST CREST JPMJCR1401 and JSPS KAKENHI Grant Numbers JP17H01788, JP18H06469, JP16K16010, JP17K19960, and JP18H05291.
Funding Information:
We thank Akitoshi Kawamura and Yukiko Yamauchi for giving an opportunity to discuss in the Open Problem Seminar at Kyushu University. This work is partially supported by JST CREST JPMJCR1401 and JSPS KAKENHI Grant Numbers JP17H01788, JP18H06469, JP16K16010, JP17K19960, and JP18H05291.
Publisher Copyright:
© Hiroshi Eto, Tesshu Hanaka, Yasuaki Kobayashi, and Yusuke Kobayashi; licensed under Creative Commons License CC-BY.
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
T2 - 14th International Symposium on Parameterized and Exact Computation, IPEC 2019
Y2 - 11 September 2019 through 13 September 2019
ER -