An optimal convex hull algorithm in any fixed dimension

Bernard Chazelle

doi:10.1007/BF02573985

An optimal convex hull algorithm in any fixed dimension

Bernard Chazelle

Research output: Contribution to journal › Article › peer-review

292 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	377-409
Number of pages	33
Journal	Discrete & Computational Geometry
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/BF02573985
State	Published - Dec 1993
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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10.1007/BF02573985

Cite this

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title = "An optimal convex hull algorithm in any fixed dimension",

abstract = "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.",

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year = "1993",

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N2 - 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.

AB - 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.

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An optimal convex hull algorithm in any fixed dimension

Abstract

All Science Journal Classification (ASJC) codes

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