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Sparse Geometric Graphs with Small Dilation

  • Boris Aronov
  • Mark de Berg
  • Otfried Cheong
  • Joachim Gudmundsson
  • Herman Haverkort
  • Antoine Vigneron
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)

Abstract

Given a set S of n points in the plane, and an integer k such that 0 ≤ k < n, we show that a geometric graph with vertex set S, at most n – 1 + k edges, and dilation O(n / (k + 1)) can be computed in time O(n log n). We also construct n–point sets for which any geometric graph with n – 1 + k edges has dilation Ω(n / (k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position.

Keywords

Span Tree Minimum Span Tree Steiner Tree Delaunay Triangulation 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

  • Boris Aronov
    • 1
  • Mark de Berg
    • 2
  • Otfried Cheong
    • 3
  • Joachim Gudmundsson
    • 4
  • Herman Haverkort
    • 2
  • Antoine Vigneron
    • 5
  1. 1.Department of Computer and Information SciencePolytechnic UniversityBrooklynUSA
  2. 2.Department of Mathematics and Computing ScienceTU EindhovenEindhovenThe Netherlands
  3. 3.Division of Computer ScienceKAISTDaejeonSouth Korea
  4. 4.IMAGEN ProgramNational ICT Australia LtdAustralia
  5. 5.Department of Computer ScienceNational University of SingaporeSingapore

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