, Volume 17, Issue 1, pp 19–32

“The big sweep”: On the power of the wavefront approach to Voronoi diagrams

  • F. Dehne
  • R. Klein

DOI: 10.1007/BF02523236

Cite this article as:
Dehne, F. & Klein, R. Algorithmica (1997) 17: 19. doi:10.1007/BF02523236


We show that the wavefront approach to Voronoi diagrams (a deterministic line-sweep algorithm that does not use geometric transform) can be generalized to distance measures more general than the Euclidean metric. In fact, we provide the first worst-case optimal (O (n logn) time,O(n) space) algorithm that is valid for the full class of what has been callednice metrics in the plane. This also solves the previously open problem of providing anO (nlogn)-time plane-sweep algorithm for arbitraryLk-metrics. Nice metrics include all convex distance functions but also distance measures like the Moscow metric, and composed metrics. The algorithm is conceptually simple, but it copes with all possible deformations of the diagram.

Key Words

Computational geometry Delaunay triangulation Voronoi diagram Sweepline 

Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • F. Dehne
    • 1
  • R. Klein
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Praktische Informatik VIFernUniversität HagenHagenGermany

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