Partitioning graphs of supply and demand

Takehiro Ito, Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

Assume that each vertex of a graph G is either a supply vertex or a demand vertex and is assigned a positive integer, called a supply or a demand. Each demand vertex can receive "power" from at most one supply vertex through edges in G. One thus wishes to partition G into connected components by deleting edges from G so that each component C has exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in C. If G does not have such a partition, one wishes to partition G into connected components so that each component C either has no supply vertex or has exactly one supply vertex whose supply is no less than the sum of demands in C, and wishes to maximize the sum of demands in all components with supply vertices. We deal with such a maximization problem, which is NP-hard even for trees and strongly NP-hard for general graphs. In this paper, we show that the problem can be solved in pseudo-polynomial time for series-parallel graphs and partial k-trees-that is, graphs with bounded tree-width.

Original languageEnglish
Pages (from-to)2620-2633
Number of pages14
JournalDiscrete Applied Mathematics
Volume157
Issue number12
DOIs
Publication statusPublished - 2009 Jun 28

Keywords

  • Demand
  • Graph partition problem
  • Partial k-tree
  • Series-parallel graph
  • Supply

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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