Journal ArticleDOI
Optimal Randomized Parallel Algorithms for Computational Geometry I
H J Reif,Sandeep Sen +1 more
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In this paper, the authors present parallel algorithms for 3-D maxima and two-set dominance counting by an application of integer sorting, which have running time of O(logn)$ using $n$ processors, with very high probability.Abstract:
We present parallel algorithms for some fundamental problems in computational geometry which have running time of $O(logn)$ using $n$ processors, with very high probability (approaching 1 as $n~ \rightarrow~ \infty$). These include planar point location, triangulation and trapezoidal decomposition. We also present optimal algorithms for 3-D maxima and two-set dominance counting by an application of integer sorting. Most of these algorithms run on CREW PRAM model and have optimal processor-time product which improve on the previously best known algorithms of Atallah and Goodrich [3] for these problems. The crux of these algorithms is a useful data structure which emulates the plane sweeping paradigm used for sequential algorithms. We extend some of the techniques used by Reischuk [22] Reif and Valiant [21] for flashsort algorithm to perform divide and conquer in a plane very efficiently leading to the improved performance by our approach.read more
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Book ChapterDOI
Parallel General Prefix Computations with Geometric, Algebraic and Other Applications
TL;DR: It is shown that general prefix techniques can be applied to a wide variety of geometric problems, including triangulation of point sets, two-set dominance counting, ECDF searching, finding two- and three-dimensional maximal points, and the (classical) reconstruction of trees from their traversals.
Posted Content
Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering
TL;DR: In this paper, a parallel algorithm for minimum spanning trees and spatial clustering hierarchies is presented, which is based on generating a well-separated pair decomposition followed by using Kruskal's minimum spanning tree algorithm and bichromatic closest pair computations.
Book ChapterDOI
Lower Bounds for Parallel Algebraic Decision Trees, Complexity of Convex Hulls and Related Problems
TL;DR: It is shown that any parallel algorithm in the fixed degree algebraic decision tree model that answers membership queries in W ⊑ R n using p processors, requires Ω(¦W¦/n log(p/n) rounds where ¦w¦ is the number of connected components of W.
References
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Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Journal ArticleDOI
A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.
Proceedings ArticleDOI
Applications of random sampling in computational geometry, II
TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.
Journal ArticleDOI
Parallel merge sort
TL;DR: A parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time; the constant in the running time is small.
Journal ArticleDOI
Optimal Search in Planar Subdivisions
TL;DR: This work presents a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely $O(\log n)$ search time with $O(n)$ storage.