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Abstract

In this paper, we consider the following variant of the geometric Steiner tree problem. Every point u which is not included in the tree costs a penalty of π(u) units. Furthermore, every Steiner point we use costs c S units. The goal is to minimize the total length of the tree plus the penalties. We prove that the problem admits a polynomial time approximation scheme, if the points lie in the plane. Our PTAS uses a new technique which allows us to bypass major requirements of Arora’s framework for approximation schemes for geometric optimization problems [1]. It may thus open new possibilities to find approximation schemes for geometric optimization problems that have a complicated topology. Furthermore the techniques we use provide a more general framework which can be applied to geometric optimization problems with more complex objective functions.

Keywords

Span Tree Approximation Scheme Side Length Steiner Tree Steiner Point 
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 2005

Authors and Affiliations

  • Jan Remy
    • 1
  • Angelika Steger
    • 1
  1. 1.Institut für Theoretische InformatikETH ZürichSwitzerland

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