Probabilistic Parallel Algorithms for Sorting and Selection

Reischuk, Rüdiger

doi:10.1137/0214030

Cited by 102 publications

(47 citation statements)

References 4 publications

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“…Meggido's [7] algorithm does maximal and median selection in constant time using a linear number of processors on the comparison tree model. Reischuk's [15] time N/ log N processor maximal selection algorithm for the CRCW PRAM model. All these results hold for the worst case input with high probability.…”

Section: Previous Resultsmentioning

confidence: 99%

Randomized parallel selection

Rajasekaran

1990

Lecture Notes in Computer Science

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We show that selection on an input of size N can be performed on a P-node hypercube (P = N/(log N)) in time O(n/P) with high probability, provided each node can process all the incident edges in one unit of time (this model is called the parallel model and has been assumed by previous researchers (e.g., [17])). This result is important in view of a lower bound of Plaxton that implies selection takes Ω((N/P)loglog P+log P) time on a P-node hypercube if each node can process only one edge at a time (this model is referred to as the sequential model). ABSTRACTWe show that selection on an input of size N can be performed on a P-node hypercube ( P = N/(log N)) in time O(N/P) with high probability, provided each node can process all the incident edges in one unit of time (this model is called the parallel model and has been assumed by previous researchers (e.g ., [17])). This result is important in view of a lower bound of Plaxton that implies selection takes Q((N/P) log log P+log P) time on a P-node hypercube if each node can process only one edge at a time (this model is referred to as the sequential model).

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Section: Previous Resultsmentioning

confidence: 99%

Randomized parallel selection

Rajasekaran

1990

Lecture Notes in Computer Science

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“…Meggido's [6] algorithm does maximal and median selection in constant time using a linear number of processors on the comparison tree model. Reischuk's [14] selection algorithm runs in O(1) time using n comparison tree processors. Floyd and Rivest's [2] sequential algorithm takes n + min(i, n − i) + o(n) time.…”

Section: Previous Resultsmentioning

confidence: 99%

Unifying Themes for Selection on Any Network

Rajasekaran

Chen

Yooseph

1997

Journal of Parallel and Distributed Computing

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“…We note that any PT-optimal algorithm for sorting must use at least log n time [4]. Reischuk [33] gives a PT-optimal randomized n processor, Θ(log n) time algorithm for sorting. Rajasekaran and Reif [30] give a randomized algorithm for general sorting which achieves Θ(log n/ log log n) time with n log ǫ n processors for any ǫ > 0, which is optimal, a randomized algorithm for integer sorting which achieves Θ(log n/ log log n) time with n(log log n) 2 / log n processors, and a PT-optimal randomized algorithm for integer sorting which achieves Θ(log n) time with n/ log n processors.…”

Section: Padded Sortmentioning

confidence: 99%

Ultrafast Expected Time Parallel Algorithms

MacKenzie

Stout

1998

Journal of Algorithms

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It has been shown previously that sorting n items into n locations with a polynomial number of processors requires Ω(log n/ log log n) time. We sidestep this lower bound with the idea of Padded Sorting, or sorting n items into n + o(n) locations. Since many problems do not rely on the exact rank of sorted items, a Padded Sort is often just as useful as an unpadded sort. Our algorithm for Padded Sort runs on the Tolerant CRCW PRAM and takes Θ(log log n/ log log log n) expected time using n log log log n/ log log n processors, assuming the items are taken from a uniform distribution. Using similar techniques we solve some computational geometry problems, including Voronoi Diagram, with the same processor and time bounds, assuming points are taken from a uniform distribution in the unit square. Further, we present an Arbitrary CRCW PRAM algorithm to solve the Closest Pair problem in constant expected time with n processors regardless of the distribution of points. All of these algorithms achieve linear speedup in expected time over their optimal serial counterparts.

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Probabilistic Parallel Algorithms for Sorting and Selection

Cited by 102 publications

References 4 publications

Randomized parallel selection

Randomized parallel selection

Unifying Themes for Selection on Any Network

Ultrafast Expected Time Parallel Algorithms

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