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(u4n) and the p-partition problem can be solved in time O(p2u4n) for any series-parallel graph of n vertices. The algorithms can be easily extended for partial k-trees, that is, graphs with bounded tree-width.
|Number of pages||12|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Publication status||Published - 2004|
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)