TY - GEN

T1 - Approximability of partitioning graphs with supply and demand

AU - Ito, Takehiro

AU - Demaine, Erik D.

AU - Zhou, Xiao

AU - Nishizeki, Takao

PY - 2006

Y1 - 2006

N2 - 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 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. The FPTAS can be easily extended for partial k-trees, that is, graphs with bounded treewidth.

AB - 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 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. The FPTAS can be easily extended for partial k-trees, that is, graphs with bounded treewidth.

UR - http://www.scopus.com/inward/record.url?scp=77249086699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77249086699&partnerID=8YFLogxK

U2 - 10.1007/11940128_14

DO - 10.1007/11940128_14

M3 - Conference contribution

AN - SCOPUS:77249086699

SN - 3540496947

SN - 9783540496946

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 121

EP - 130

BT - Algorithms and Computation - 17th International Symposium, ISAAC 2006, Proceedings

T2 - 17th International Symposium on Algorithms and Computation, ISAAC 2006

Y2 - 18 December 2006 through 20 December 2006

ER -