TY - JOUR

T1 - Partitioning graphs of supply and demand

AU - Ito, Takehiro

AU - Zhou, Xiao

AU - Nishizeki, Takao

PY - 2009/6/28

Y1 - 2009/6/28

N2 - 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.

AB - 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.

KW - Demand

KW - Graph partition problem

KW - Partial k-tree

KW - Series-parallel graph

KW - Supply

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U2 - 10.1016/j.dam.2008.08.012

DO - 10.1016/j.dam.2008.08.012

M3 - Article

AN - SCOPUS:67349109764

SN - 0166-218X

VL - 157

SP - 2620

EP - 2633

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 12

ER -