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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)

Abstract

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.

Keywords

Planar Graph Central Node Edge Incident Graph Drawing Leaf Edge 
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 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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