Minimum cost subpartitions in graphs

Given an edge-weighted graph G = (V,E), a subset S ⊆ V , an integer k 1 and a real b 0, the minimum subpartition problem asks to find a family of k nonempty disjoint subsets X1,X2,...,Xk ⊆ S with d(Xi) b, 1 i k, so as to minimize 1 i k d(Xi), where d(X) denotes the total weight of edges between X and V − X. In this paper, we show that the minimum subpartition problem can be solved in O(mn + n2 logn) time. The result is then applied to the minimum k-way cut problem and the graph strength problem to improve the previous best time bounds of 2-approximation algorithms for these problems to O(mn + n2 logn). © 2006 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Hiroshi Nagamochi, Yoko Kamidoi
• Keywords: Edge-weighted Graph, IPL 2007, Minimum Subpartition Problem, Nonempty Disjoint Subsets