An optimal convex hull algorithm in any fixed dimension

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254 Scopus citations


We present a deterministic algorithm for computing the convex hull of n points in E d in optimal O(n log n+n {down left corner}d/2{down right corner} ) time. Optimal solutions were previously known only in even dimension and in dimension 3. A by-product of our result is an algorithm for computing the Voronoi diagram of n points in d-space in optimal O(n log n+n {top left corner}d/2{top right corner} ) time.

Original languageEnglish (US)
Pages (from-to)377-409
Number of pages33
JournalDiscrete & Computational Geometry
Issue number1
StatePublished - Dec 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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