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SpaceEfficient Geometric DivideandConquer Algorithms
, 2004
"... We present an approach to simulate divideandconquer algorithms in a spaceefficient way, and illustrate it by giving spaceefficient algorithms for the closestpair, bichromatic closestpair, allnearestneighbors, and orthogonal line segment intersection problems. ..."
Abstract

Cited by 15 (4 self)
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We present an approach to simulate divideandconquer algorithms in a spaceefficient way, and illustrate it by giving spaceefficient algorithms for the closestpair, bichromatic closestpair, allnearestneighbors, and orthogonal line segment intersection problems.
Speculative Parallelization of a Randomized Incremental Convex Hull Algorithm
 Proc. Int’l Workshop Computational Geometry and Applications
, 2004
"... Abstract. Finding the fastest algorithm to solve a problem is one of the main issues in Computational Geometry. Focusing only on worst case analysis or asymptotic computations leads to the development of complex data structures or hard to implement algorithms. Randomized algorithms appear in this sc ..."
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Cited by 5 (4 self)
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Abstract. Finding the fastest algorithm to solve a problem is one of the main issues in Computational Geometry. Focusing only on worst case analysis or asymptotic computations leads to the development of complex data structures or hard to implement algorithms. Randomized algorithms appear in this scenario as a very useful tool in order to obtain easier implementations within a good expected time bound. However, parallel implementations of these algorithms are hard to develop and require an indepth understanding of the language, the compiler and the underlying parallel computer architecture. In this paper we show how we can use speculative parallelization techniques to execute in parallel iterative algorithms such as randomized incremental constructions. In this paper we focus on the convex hull problem, and show that, using our speculative parallelization engine, the sequential algorithm can be automatically executed in parallel, obtaining speedups with as little as four processors, and reaching 5.15x speedup with 28 processors. 1
unknown title
, 2004
"... 1 Introduction Researchers have studied spaceefficient algorithms since the early 1970's. Examples include merging, (multiset) sorting, and partitioning problems; see, for example, references [9, 13, 12]. Br"onnimann et al. [5] were the first to consider spaceefficient geometric alg ..."
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1 Introduction Researchers have studied spaceefficient algorithms since the early 1970's. Examples include merging, (multiset) sorting, and partitioning problems; see, for example, references [9, 13, 12]. Br&quot;onnimann et al. [5] were the first to consider spaceefficient geometric algorithms and showed how to compute the convex hull of aplanar set of n points in O(n log h) time using O(1) extra space, where h denotes the size of the output(the number of extreme points). Recently, Chen and Chan [6] addressed the problem of computing all the
SpaceEfficient Geometric DivideandConquer Algorithms ⋆ Prosenjit Bose a Anil Maheshwari a
"... We develop a number of spaceefficient tools including an approach to simulate divideandconquer spaceefficiently, stably selecting and unselecting a subset from a sorted set, and computing the kth smallest element in one dimension from a multidimensional set that is sorted in another dimension. ..."
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We develop a number of spaceefficient tools including an approach to simulate divideandconquer spaceefficiently, stably selecting and unselecting a subset from a sorted set, and computing the kth smallest element in one dimension from a multidimensional set that is sorted in another dimension. We then apply these tools to solve several geometric problems that have solutions using some form of divideandconquer. Specifically, we present a deterministic algorithm running in O(n log n) time using O(1) extra memory given inputs of size n for the closest pair problem and a randomized solution running in O(n log n) expected time and using O(1) extra space for the bichromatic closest pair problem. For the orthogonal line segment intersection problem, we solve the problem in O(n log n + k) time using O(1) extra space where n is the number of horizontal and vertical line segments and k is the number of intersections. 1