Generalized k-multiway cut problems

This paper considers the following problem: given an edge-weighted graph G = (V, E, w) and disjoint k-subsets Up of V, find a minimum weighted set of edges E′ ⊆ CE such that its removal disconnects the graph into k parts and each part contains exactly one vertex from each Up for 1 ≤ p ≤ r. This generalizes some well-known NP-hard problems. In this paper, we first apply greedy local search algorithm to obtain better approximation solutions, Then we give a randomized local search algorithm which produces a solution within a factor (1 + ε) with the probability at least (1 - 1/e) for any small ε. Simple near-optimum approximation algorithms are also proposed. Analogously, there is a maximum k-multiway cut problem with the same restrictions. © 2006 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.