A Linear time algorithm for computing the Voronoi diagram of a convex polygon

Authors:
A. Aggarwal;L. Guibas;J. Saxe;P. Shor
Affiliations:
IBM T. J. Watson Center Yorktown Heights, NY;Stanford University, Stanford, CA and DEC Systems Research Center, Palo Alto, CA;DEC Systems Research Center, Palo Alto, CA;AT&T Bell Labs, Murray Hill, NJ
Venue:
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Year:
1987

Citing 4
Cited 13

Computational geometry: an introduction

Computational geometry: an introduction
Primitives for the manipulation of general subdivisions and the computation of Voronoi

ACM Transactions on Graphics (TOG)
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees

Journal of the ACM (JACM)
Computational geometry.

Computational geometry.

Fining k points with minimum spanning trees and related problems

SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Output sensitive construction of levels and Voronoi diagrams in Rd of order 1 to k

STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Solving query-retrieval problems by compacting Voronoi diagrams

STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Randomized multidimensional search trees (extended abstract): dynamic sampling

SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Selection and sorting in totally monotone arrays

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Base station placement on boundary of a convex polygon

Journal of Parallel and Distributed Computing
On multiplicatively weighted Voronoi diagrams for lines in the plane

Transactions on computational science XIII
Efficient algorithm for placing base stations by avoiding forbidden zone

ICDCIT'05 Proceedings of the Second international conference on Distributed Computing and Internet Technology
Efficient large-scale terrain rendering method for real-world game simulation

Edutainment'06 Proceedings of the First international conference on Technologies for E-Learning and Digital Entertainment
An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem

Discrete Optimization
Voronoi diagram with visual restriction

FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Localized geometric query problems

Computational Geometry: Theory and Applications
An approximation algorithm for k-center problem on a convex polygon

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present an algorithm for computing certain kinds of three-dimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram of n points in the plane can be computed in &THgr;(n) time when these points form the vertices of a convex polygon in, say, counterclockwise order. This settles an outstanding open problem in computational geometry. Our techniques can also be used to obtain linear time algorithms for computing the farthest-point Voronoi diagram and the medial axis of a convex polygon and for deleting a vertex from a general planar Voronoi diagram.