## 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(u^{4}n) and the p-partition problem can be solved in time O(p^{2}u^{4}n) 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.

Original language | English |
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Pages (from-to) | 365-376 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 3353 |

DOIs | |

Publication status | Published - 2004 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)