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Randomized Algorithms for Binary Search and Load Balancing on Fixed Connection Networks With Geometric Applications
, 1990
"... There are now a number of fundamental problems in computational geometry that have optimal algorithms on PRAM models. We present randomized parallel algorithms which execute on an nprocessor buttery interconnection network in O(log n) time for the following problems of input size n: trapezoidal ..."
Abstract

Cited by 18 (2 self)
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There are now a number of fundamental problems in computational geometry that have optimal algorithms on PRAM models. We present randomized parallel algorithms which execute on an nprocessor buttery interconnection network in O(log n) time for the following problems of input size n: trapezoidal decomposition, visibility, triangulation and 2D convex hull. These algorithms involve tackling some of the very basic problems like binary search and loadbalancing that we take for granted in PRAM models. Apart from a 2D convex hull algorithm, these are the rst nontrivial geometric algorithms which attain this performance on xed connection networks. Our techniques use a number of ideas from Flashsort which have to be modied to handle more dicult situations; it seems likely that they will have wider applications. 1 Introduction 1.1 Motivation and overview In the past decade, we have witnessed a systematic growth in the stateofart of parallelizing algorithms in the PRAM envi...
Parallel techniques for computational geometry
 Proc. IEEE
, 1992
"... A survey of techniques for solving geometric problems in parallel is given, both for shared memory parallel machines and for networks of processors. Open problems are also discussed, as well as directions for future research. 'This work was supported by the office oi Naval Research under Contracts N ..."
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Cited by 13 (0 self)
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A survey of techniques for solving geometric problems in parallel is given, both for shared memory parallel machines and for networks of processors. Open problems are also discussed, as well as directions for future research. 'This work was supported by the office oi Naval Research under Contracts N0001484K0502 and
Highly Parallelizable Problems (Extended Abstract)
"... ) Omer Berkman 1,4 Dany Breslauer 1,2 Zvi Galil 1,2 Baruch Schieber 3 Uzi Vishkin 1,4,5 Summary of Results. We establish that several problems are highly parallelizable. For each of these problems, we design an optimal O (loglogn ) time parallel algorithm on the Common CRCW PRAM model which ..."
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Cited by 2 (0 self)
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) Omer Berkman 1,4 Dany Breslauer 1,2 Zvi Galil 1,2 Baruch Schieber 3 Uzi Vishkin 1,4,5 Summary of Results. We establish that several problems are highly parallelizable. For each of these problems, we design an optimal O (loglogn ) time parallel algorithm on the Common CRCW PRAM model which is the weakest among the CRCW PRAM models. These problems include: # all nearest smaller values, # preprocessing for answering range maxima queries, # several problems in Computational Geometry, # string matching. Until recently, such algorithms were known only for finding the maximum and merging. A new lower bound technique is presented showing that some of the new O (loglogn ) upper bounds cannot be improved even when non optimal algorithms are used. The technique extends Ramseylike lower bound argumentation due to auf der Heide and Wigderson [MW85]. Its most interesting applications are for Computational Geometry problems for which no previous lower bounds are known. ###############...
Lower bounds for intersection searching and fractional cascading in higher dimension $
, 2001
"... Given an nedge convex subdivision of the plane, is it possible to report its k intersections witha query line segment in Oðk þ polylogðnÞÞ time, using subquadratic storage? If the query is a plane and the input is a polytope with n vertices, can one achieve Oðk þ polylogðnÞÞ time withsubcubic stora ..."
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Given an nedge convex subdivision of the plane, is it possible to report its k intersections witha query line segment in Oðk þ polylogðnÞÞ time, using subquadratic storage? If the query is a plane and the input is a polytope with n vertices, can one achieve Oðk þ polylogðnÞÞ time withsubcubic storage? Does any convex polytope have a boundary dominant Dobkin–Kirkpatrick hierarchy? Can fractional cascading be generalized to planar maps instead of linear lists? We prove that the answer to all of these questions is no, and we derive nearoptimal solutions to these classical problems. r 2003 Elsevier Inc. All rights reserved. 1.
(Preliminary Version)
"... Randomized algorithms for binary search and load balancing on fixed connection networks ..."
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Randomized algorithms for binary search and load balancing on fixed connection networks