Journal ArticleDOI
The all nearest-neighbor problem for convex polygons
Der-Tsai Lee,Franco P. Preparata +1 more
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This article is published in Information Processing Letters.The article was published on 1978-06-01. It has received 37 citations till now. The article focuses on the topics: Convex set & Convex polytope.read more
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Geometric applications of a matrix-searching algorithm
TL;DR: The Θ(m) bound on finding the maxima of wide totally monotone matrices is used to speed up several geometric algorithms by a factor of logn.
Journal ArticleDOI
Computational Geometry—A Survey
TL;DR: The state of the art of computational geometry is surveyed, a discipline that deals with the complexity of geometric problems within the framework of the analysis of algorithms.
Journal ArticleDOI
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees
TL;DR: Sous l'hypothese que trois points d'entree ne forment pas un triangle isocele, le RNG de n points dans un espace dimension r peut etre trouve en un temps O(n 2 ) pour r≥3.
Proceedings ArticleDOI
Geometric applications of a matrix searching algorithm
TL;DR: The Θ(m) bound on finding the maxima of wide totally monotone matrices is used to speed up several geometric algorithms by a factor of logn.
References
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Proceedings ArticleDOI
Closest-point problems
Michael Ian Shamos,Dan Hoey +1 more
TL;DR: The purpose of this paper is to introduce a single geometric structure, called the Voronoi diagram, which can be constructed rapidly and contains all of the relevant proximity information in only linear space, and is used to obtain O(N log N) algorithms for most of the problems considered.
Proceedings ArticleDOI
Geometric complexity
TL;DR: An effort is made to recast classical theorems into a useful computational form and analogies are developed between constructibility questions in Euclidean geometry and computability questions in modern computational complexity.
Proceedings ArticleDOI
Divide-and-conquer in multidimensional space
TL;DR: A divide-and-conquer technique in multidimensional space is investigated which decomposes a geometric problem into two problems on N/2 points in k dimensions plus a single problem in k−1 dimension to obtain an algorithm for finding the two closest of N points in 0(N log N) time in any dimension.