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Spanning Distribution Trees of Graphs

(Extended Abstract)
  • Masaki Kawabata
  • Takao Nishizeki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7924)

Abstract

Let G be a graph with a single source w, assigned a positive integer called the supply. Every vertex other than w is a sink, assigned a nonnegative integer called the demand. Every edge is assigned a positive integer called the capacity. Then a spanning tree T of G is called a spanning distribution tree if the capacity constraint holds when, for every sink v, an amount of flow, equal to the demand of v, is sent from w to v along the path in T between them. The spanning distribution tree problem asks whether a given graph has a spanning distribution tree or not. In the paper, we first observe that the problem is NP-complete even for series-parallel graphs, and then give a pseudo-polynomial time algorithm to solve the problem for a given series-parallel graph G.

Keywords

spanning distribution tree series-parallel graph flow supply demand partial k-tree 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Masaki Kawabata
    • 1
  • Takao Nishizeki
    • 1
  1. 1.School of Science and TechnologyKwansei Gakuin UniversitySandaJapan

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