Partitioning a graph of bounded tree-width to connected subgraphs of almost uniform size

Takehiro Ito, Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticle

12 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 wishes 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 analogously; and 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, respectively, 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 with n vertices. The algorithms can be extended for partial k-trees, that is, graphs with bounded tree-width.

Original languageEnglish
Pages (from-to)142-154
Number of pages13
JournalJournal of Discrete Algorithms
Volume4
Issue number1
DOIs
Publication statusPublished - 2006 Mar 1

Keywords

  • (l,u)-partition
  • Algorithm
  • Lower bound
  • Maximum partition problem
  • Minimum partition problem
  • Partial k-tree
  • Series-parallel graph
  • Upper bound

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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