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How to Morph Planar Graph Drawings

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  • Soroush Alamdari, Cornell Univ, Cornell University, Dept Comp Sci
  • ,
  • Patrizio Angelini, Tubingen Univ, Eberhard Karls University of Tubingen, Wilhelm Schickard Inst Informat
  • ,
  • Fidel Barrera-Cruz, Georgia Institute of Technology
  • ,
  • Timothy M. Chan, University of Waterloo
  • ,
  • Giordano Da Lozzo, University of California at Irvine
  • ,
  • Giuseppe Di Battista, Roma Tre University
  • ,
  • Fabrizio Frati, Roma Tre University
  • ,
  • Penny Haxell, University of Waterloo
  • ,
  • Anna Lubiw, University of Waterloo
  • ,
  • Maurizio Patrignani, Roma Tre University
  • ,
  • Vincenzo Roselli, Roma Tre University
  • ,
  • Sahil Singla, Carnegie Mellon Univ, Carnegie Mellon University, Sch Comp Sci
  • ,
  • Bryan T. Wilkinson

Given an n-vertex graph and two straight-line planar drawings of the graph that have the same faces and the same outer face, we show that there is a morph (i.e., a continuous transformation) between the two drawings that preserves straight-line planarity and consists of O(n) steps, which we prove is optimal in the worst case. Each step is a unidirectional linear morph, which means that every vertex moves at constant speed along a straight line, and the lines are parallel although the vertex speeds may differ. Thus we provide an efficient version of Cairns' 1944 proof of the existence of straight-line planarity-preserving morphs for triangulated graphs, which required an exponential number of steps.

Original languageEnglish
JournalS I A M Journal on Computing
Pages (from-to)824-852
Number of pages29
Publication statusPublished - 2017

    Research areas

  • INTERPOLATION, TRIANGULATIONS, morph, planar graphs, transformation

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