Paper by Erik D. Demaine

Reference:

Takehiro Ito, Erik D. Demaine, Xiao Zhou, and Takao Nishizeki, “Approximability of Partitioning Graphs with Supply and Demand”, in Proceedings of the 17th Annual International Symposium on Algorithms and Computation (ISAAC 2006), Lecture Notes in Computer Science, volume 4288, Calcutta, India, December 18–20, 2006, pages 121–130.

BibTeX

@InProceedings{SupplyDemand_ISAAC2006,
  AUTHOR        = {Takehiro Ito and Erik D. Demaine and Xiao Zhou and
                   Takao Nishizeki},
  TITLE         = {Approximability of Partitioning Graphs
                   with Supply and Demand},
  BOOKTITLE     = {Proceedings of the 17th Annual International Symposium on
                   Algorithms and Computation (ISAAC 2006)},
  bookurl       = {http://www.isical.ac.in/~isaac06},
  VOLUME        = 4288,
  SERIES        = {Lecture Notes in Computer Science},
  seriesurl     = {http://www.springer.de/comp/lncs/},
  ADDRESS       = {Calcutta, India},
  MONTH         = {December 18--20},
  YEAR          = 2006,
  PAGES         = {121--130},

  papers        = {SupplyDemand_JDA},
  copyright     = {The paper is \copyright Springer-Verlag.},
  doi           = {https://dx.doi.org/10.1007/11940128_14},
  dblp          = {https://dblp.org/rec/conf/isaac/ItoDZN06},
  comments      = {This paper is also available from <A HREF="http://dx.doi.org/10.1007/11940128_14">SpringerLink</A>.},
}

Abstract:

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.

Comments:

This paper is also available from SpringerLink.

Copyright:

The paper is \copyright Springer-Verlag.

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SupplyDemand_JDA (Approximability of Partitioning Graphs with Supply and Demand)