Succinct Greedy Drawings Do Not Always Exist

  • Patrizio Angelini
  • Giuseppe Di Battista
  • Fabrizio Frati
Conference paper

DOI: 10.1007/978-3-642-11805-0_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)
Cite this paper as:
Angelini P., Di Battista G., Frati F. (2010) Succinct Greedy Drawings Do Not Always Exist. In: Eppstein D., Gansner E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg

Abstract

A greedy drawing is a graph drawing containing a distance-decreasing path for every pair of nodes. A path (v0,v1,...,vm) is distance-decreasing if d(vi,vm) < d(vi − 1,vm), 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.

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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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