Approximability of partitioning graphs with supply and demand

Takehiro Ito, Erik D. Demaine, Xiao Zhou, Takao Nishizeki

研究成果: Article査読

20 被引用数 (Scopus)

抄録

Suppose that each vertex of a graph G is either a supply vertex or a demand vertex and is assigned a positive real number, called the supply or the 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 either has no supply vertex or has exactly one supply vertex whose supply is at least the sum of demands in C, and wishes to maximize the fulfillment, that is, the sum of demands in all components with supply vertices. This maximization problem is known to be NP-hard even for trees having exactly one supply vertex and strongly NP-hard for general graphs. In this paper, we focus on the approximability of the problem. We first show that the problem is MAXSNP-hard and hence there is no polynomial-time approximation scheme (PTAS) for general graphs unless P = NP. We then present a fully polynomial-time approximation scheme (FPTAS) for series-parallel graphs having exactly one supply vertex.

本文言語English
ページ(範囲)627-650
ページ数24
ジャーナルJournal of Discrete Algorithms
6
4
DOI
出版ステータスPublished - 2008 12

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 離散数学と組合せ数学
  • 計算理論と計算数学

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