eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-18
60:1
60:14
10.4230/LIPIcs.MFCS.2020.60
article
Efficient Enumerations for Minimal Multicuts and Multiway Cuts
Kurita, Kazuhiro
1
https://orcid.org/0000-0002-7638-3322
Kobayashi, Yasuaki
2
https://orcid.org/0000-0003-3244-6915
National Institute of Informatics, Tokyo, Japan
Kyoto University, Japan
Let G = (V, E) be an undirected graph and let B ⊆ V × V be a set of terminal pairs. A node/edge multicut is a subset of vertices/edges of G whose removal destroys all the paths between every terminal pair in B. The problem of computing a minimum node/edge multicut is NP-hard and extensively studied from several viewpoints. In this paper, we study the problem of enumerating all minimal node multicuts. We give an incremental polynomial delay enumeration algorithm for minimal node multicuts, which extends an enumeration algorithm due to Khachiyan et al. (Algorithmica, 2008) for minimal edge multicuts.
Important special cases of node/edge multicuts are node/edge multiway cuts, where the set of terminal pairs contains every pair of vertices in some subset T ⊆ V, that is, B = T × T. We improve the running time bound for this special case: We devise a polynomial delay and exponential space enumeration algorithm for minimal node multiway cuts and a polynomial delay and space enumeration algorithm for minimal edge multiway cuts.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol170-mfcs2020/LIPIcs.MFCS.2020.60/LIPIcs.MFCS.2020.60.pdf
Multicuts
Multiway cuts
Enumeration algorithms