Partitioning aweighted tree into subtrees with weights in a given range

Takehiro Ito, Takao Nishizeki, Michael Schröder, Takeaki Uno, Xiao Zhou

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l andu are given integers such that 0 ≤ l≤ u. 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 a 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 given number p of components. All these problems are NP-hard even for series-parallel graphs, but are solvable in linear time for paths. In this paper, we present the first polynomial-time algorithm to solve the three problems for arbitrary trees.

Original languageEnglish
Pages (from-to)823-841
Number of pages19
Issue number3-4
Publication statusPublished - 2012 Apr 1


  • Algorithm
  • Dynamic programming
  • Fast Fourier transform
  • Graph partition
  • Polynomial-time
  • Subtree
  • Tree

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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