Partitioning trees of supply and demand

Takehiro Ito, Xiao Zhou, Takao Nishizeki

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

6 Citations (Scopus)

Abstract

Assume that a tree T has a number ns of "supply vertices" and all the other vertices are "demand vertices." Each supply vertex is assigned a positive number called a supply, while each demand vertex is assigned a positive number called a demand. One wish to partition T into exactly ns subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in the subtree. The "partition problem" is a decision problem to ask whether T has such a partition. The "maximum partition problem" is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. First is a linear-time algorithm for the partition problem. Second is a pseudo-polynomial-time algorithm for the maximum partition problem. Third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings
Pages612-623
Number of pages12
DOIs
Publication statusPublished - 2002 Dec 1
Event13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 - Vancouver, BC, Canada
Duration: 2002 Nov 212002 Nov 23

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2518 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th Annual International Symposium on Algorithms and Computation, ISAAC 2002
CountryCanada
CityVancouver, BC
Period02/11/2102/11/23

Keywords

  • Algorithm
  • Approximation
  • Demand
  • FPTAS
  • Maximum partition problem
  • Partition problem
  • Supply
  • Tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Ito, T., Zhou, X., & Nishizeki, T. (2002). Partitioning trees of supply and demand. In Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings (pp. 612-623). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS). https://doi.org/10.1007/3-540-36136-7_53