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Minimum Average Distance Triangulations

  • László Kozma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)

Abstract

We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x and y along edges of T, with edge weights given as part of the problem. In a different variant of the problem, the points are vertices of a simple polygon and we look for a triangulation of the interior of the polygon that is optimal in the same sense. We prove that a general formulation of the problem in which the weights are arbitrary positive numbers is strongly NP-complete. For the case when all weights are equal we give polynomial-time algorithms. In the end we mention several open problems.

Keywords

Short Path Network Design Problem Steiner Point Wiener Index Simple Polygon 
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 2012

Authors and Affiliations

  • László Kozma
    • 1
  1. 1.Universität des SaarlandesSaarbrückenGermany

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