Partitioning a weighted tree to subtrees of almost uniform size

Takehiro Ito, Takeaki Uno, Xiao Zhou, Takao Nishizeki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are 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 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 given number p of components. All these problems are NP-hard even for series-parallel graphs, but are solvable for paths in linear time and for trees in polynomial time. In this paper, we give polynomial-time algorithms to solve the three problems for trees, which are much simpler and faster than the known algorithms.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 19th International Symposium, ISAAC 2008, Proceedings
Pages196-207
Number of pages12
DOIs
Publication statusPublished - 2008 Dec 1
Event19th International Symposium on Algorithms and Computation, ISAAC 2008 - Gold Coast, QLD, Australia
Duration: 2008 Dec 152008 Dec 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5369 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th International Symposium on Algorithms and Computation, ISAAC 2008
CountryAustralia
CityGold Coast, QLD
Period08/12/1508/12/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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