Minimum Length Embedding of Planar Graphs at Fixed Vertex Locations

  • Timothy M. Chan
  • Hella-Franziska Hoffmann
  • Stephen Kiazyk
  • Anna Lubiw
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)

Abstract

We consider the problem of finding a planar embedding of a graph at fixed vertex locations that minimizes the total edge length. The problem is known to be NP-hard. We give polynomial time algorithms achieving an \(O(\sqrt{n} \log n)\) approximation for paths and matchings, and an O(n) approximation for general graphs.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Timothy M. Chan
    • 1
  • Hella-Franziska Hoffmann
    • 1
  • Stephen Kiazyk
    • 1
  • Anna Lubiw
    • 1
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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