Approximation Schemes for Capacitated Geometric Network Design

  • Anna Adamaszek
  • Artur Czumaj
  • Andrzej Lingas
  • Jakub Onufry Wojtaszczyk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

We study a capacitated network design problem in geometric setting. We assume that the input consists of an integral link capacity k and two sets of points on a plane, sources and sinks, each source/sink having an associated integral demand (amount of flow to be shipped from/to). The capacitated geometric network design problem is to construct a minimum-length network N that allows to route the requested flow from sources to sinks, such that each link in N has capacity k; the flow is splittable and parallel links are allowed in N.

The capacitated geometric network design problem generalizes, among others, the geometric Steiner tree problem, and as such it is NP-hard.

We show that if the demands are polynomially bounded and the link capacity k is not too large, the single-sink capacitated geometric network design problem admits a polynomial-time approximation scheme. If the capacity is arbitrarily large, then we design a quasi-polynomial time approximation scheme for the capacitated geometric network design problem allowing for arbitrary number of sinks. Our results rely on a derivation of an upper bound on the number of vertices different from sources and sinks (the so called Steiner vertices) in an optimal network. The bound is polynomial in the total demand of the sources.

Keywords

Approximation Scheme Network Design Total Demand Link Capacity Network Design Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Anna Adamaszek
    • 1
  • Artur Czumaj
    • 1
  • Andrzej Lingas
    • 2
  • Jakub Onufry Wojtaszczyk
    • 3
  1. 1.DIMAP and Department of Computer ScienceUniversity of WarwickUK
  2. 2.Department of Computer ScienceLund UniversitySweden
  3. 3.Google, Inc.USA

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