Approximation Algorithms for Feasible Cut and Multicut Problems
نویسندگان
چکیده
Let G = (V; E) be an undirected graph with a capacity function u : E!< + and let S 1 ; S 2 ; : : : ; S k be k commodities, where each S i consists of a pair of nodes. A set X of nodes is called feasible if it contains no S i , and a cut (X; X) is called feasible if X is feasible. Several optimization problems on feasible cuts are shown to be NP-hard. A 2-approximation algorithm for the minimum-capacity feasible v-cut problem is presented. The multicut problem is to nd a set of edges F E of minimum capacity such that no connected component of G nF contains a commodity S i. It is shown that an ?approximation algorithm for the minimum-ratio feasible cut problem gives a 2(1 + ln T)-approximation algorithm for the multicut problem, where T denotes the cardinality of S i S i. A new approximation guarantee of O(t log T) for the minimum capacity-to-demand ratio Steiner cut problem is presented; here each commodity S i is a set of two or more nodes and t denotes the maximum cardinality of a commodity S i. N2L 3G1. Supported in part by NSERC grant no. OGP0138432 (NSERC code OGPIN 007). y A preliminary version of this paper has appeared in: \Approximation algorithms for feasible cut and multicut problems", Proc.
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