Succinct Greedy Drawings Do Not Always Exist

  • Patrizio Angelini
  • Giuseppe Di Battista
  • Fabrizio Frati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)


A greedy drawing is a graph drawing containing a distance-decreasing path for every pair of nodes. A path (v 0,v 1,...,v m ) is distance-decreasing if d(v i ,v m ) < d(v i − 1,v m ), for i = 1,...,m. Greedy drawings easily support geographic greedy routing. Hence, a natural and practical problem is the one of constructing greedy drawings in the plane using few bits for representing vertex Cartesian coordinates and using the Euclidean distance as a metric. We show that there exist greedy-drawable graphs that do not admit any greedy drawing in which the Cartesian coordinates have less than a polynomial number of bits.


Planar Graph Central Node Edge Incident Graph Drawing Leaf Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Giuseppe Di Battista
    • 1
  • Fabrizio Frati
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneRoma Tre UniversityItaly

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