Partitioning a Weighted Graph to Connected Subgraphs of Almost Uniform Size

Abstract. Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wish to partition G into connected components by deleting edges from G so that the total weight of each component is at least l and at most u. Such an “almost uniform” partition is called an (l, u)-partition. We deal with three problems to find an (l, u)-partition of a given graph. The minimum partition problem is to find an (l, u)-partition with the minimum number of components. The maximum partition problem is defined similarly. The p-partition problem is to find an (l, u)-partition with a fixed number p of components. All these problems are NP-complete or NP-hard even for series-parallel graphs. In this paper we show that both the minimum partition problem and the maximum partition problem can be solved in time O(u4 n) and the p-partition problem can be solved in time O(p2 u4 n) for any series-parallel graph of n vertices. The algorithms can...

• Type: Conference
• Year: 2004
• Where: WG
• Authors: Takehiro Ito, Xiao Zhou, Takao Nishizeki
• Keywords: Computer Science, Maximum Partition Problem, Minimum Partition Problem, Partition Problem, WG 2004