Partitioning a weighted graph to connected subgraphs of almost uniform size

Takehiro Ito, Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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(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.

Original languageEnglish
Pages (from-to)365-376
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3353
DOIs
Publication statusPublished - 2004

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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