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Discrete & Computational Geometry

, Volume 42, Issue 3, pp 489–516 | Cite as

Schnyder Woods for Higher Genus Triangulated Surfaces, with Applications to Encoding

  • Luca Castelli Aleardi
  • Éric Fusy
  • Thomas Lewiner
Article

Abstract

Schnyder woods are a well-known combinatorial structure for plane triangulations, which yields a decomposition into three spanning trees. We extend here definitions and algorithms for Schnyder woods to closed orientable surfaces of arbitrary genus. In particular, we describe a method to traverse a triangulation of genus g and compute a so-called g-Schnyder wood on the way. As an application, we give a procedure to encode a triangulation of genus g and n vertices in 4n+O(glog (n)) bits. This matches the worst-case encoding rate of Edgebreaker in positive genus. All the algorithms presented here have execution time O((n+g)g) and hence are linear when the genus is fixed.

Keywords

Schnyder woods Triangulations Higher genus surfaces Graph encoding 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Luca Castelli Aleardi
    • 1
  • Éric Fusy
    • 1
    • 2
  • Thomas Lewiner
    • 3
  1. 1.École PolytechniqueParisFrance
  2. 2.University of British ColumbiaVancouverCanada
  3. 3.Department of MathematicsPUC-RioRio de JaneiroBrazil

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