Approximating the Average Stretch Factor of Geometric Graphs

  • Siu-Wing Cheng
  • Christian Knauer
  • Stefan Langerman
  • Michiel Smid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6506)


Let G be a geometric graph whose vertex set S is a set of n points in ℝ d . The stretch factor of two distinct points p and q in S is the ratio of their shortest-path distance in G and their Euclidean distance. We consider the problem of approximating the sum of all \(n \choose 2\) stretch factors determined by all pairs of points in S. We show that for paths, cycles, and trees, this sum can be approximated, within a factor of 1 + ε, in O(n polylog(n)) time. For plane graphs, we present a (2 + ε)-approximation algorithm with running time O(n 5/3 polylog(n)), and a (4 + ε)-approximation algorithm with running time O(n 3/2 polylog(n)).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Siu-Wing Cheng
    • 1
  • Christian Knauer
    • 2
  • Stefan Langerman
    • 3
  • Michiel Smid
    • 4
  1. 1.Department of Computer Science and EngineeringHKUSTHong Kong
  2. 2.Institute of Computer ScienceUniversität BayreuthGermany
  3. 3.Département d’InformatiqueUniversité Libre de BruxellesBelgium
  4. 4.School of Computer ScienceCarleton UniversityOttawaCanada

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