Algorithmica

, Volume 15, Issue 3, pp 223–241

Incremental topological flipping works for regular triangulations

Authors

  • H. Edelsbrunner
    • Department of Computer ScienceUniversity of Illinois at Urbana-Champaign
  • N. R. Shah
    • Department of Computer ScienceUniversity of Illinois at Urbana-Champaign
Article

DOI: 10.1007/BF01975867

Cite this article as:
Edelsbrunner, H. & Shah, N.R. Algorithmica (1996) 15: 223. doi:10.1007/BF01975867

Abstract

A set ofn weighted points in general position in ℝd defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next point, then the algorithm takes expected time at mostO(nlogn+n[d/2]). Under the assumption that the points and weights are independently and identically distributed, the expected running time is between proportional to and a factor logn more than the expected size of the regular triangulation. The expectation is over choosing the points and over independent coin-flips performed by the algorithm.

Key words

Geometric algorithmsGrid generationRegular and Delaunay triangulationsFlippingTopological orderPoint locationIncrementalRandomized

Copyright information

© Springer-Verlag New York Inc. 1996