Partitioning graphs of supply and demand

Takehiro Ito, Xiao Zhou, Takao Nishizeki

研究成果: Article査読

11 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2620-2633
ページ数14
ジャーナルDiscrete Applied Mathematics
157
12
DOI
出版ステータスPublished - 2009 6 28

ASJC Scopus subject areas

  • 離散数学と組合せ数学
  • 応用数学

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