Improved deterministic parallel integer sorting

Bhatt, Pramod Chandra P.; Diks, Krzysztof; Hagerup, Torben; Prasad, V.C.; Radzik, Tomasz; Saxena, Sanjeev

doi:10.1016/0890-5401(91)90031-v

Cited by 99 publications

(81 citation statements)

References 12 publications

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“…Lemma 5 [2] n numbers in the range [0, n c ] can be sorted in O(log n) time using n log n log log n CRCW PRAM processors, as long as c is a constant.…”

Section: Lemma 2 If a Problem Can Be Solved In Time T Using P Processmentioning

confidence: 99%

Parallel algorithms for relational coarsest partition problems

Rajasekaran

Lee

1998

IEEE Trans. Parallel Distrib. Syst.

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Relational Coarsest Partition Problems (RCPPs) play a vital role in verifying concurrent systems. It is known that RCPPs are P-complete and hence it may not be possible to design polylog time parallel algorithms for these problems.In this paper, we present a parallel algorithm for RCPP, in which its associated label transition system is assumed to have m transitions and n states. This algorithm runs in O(n 1+ ) time using m n EREW PRAM processors, for any fixed < 1. This algorithm is analogous and optimal with respect to the sequential algorithm of Kanellakis and Smolka. The same algorithm runs in time O(n log n) using m log n log log n CRCW PRAM processors. We also describe implementation and experimental results on performance of our algorithm.

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“…Lemma 5 [2] n numbers in the range [0, n c ] can be sorted in O(log n) time using n log n log log n CRCW PRAM processors, as long as c is a constant.…”

Section: Lemma 2 If a Problem Can Be Solved In Time T Using P Processmentioning

confidence: 99%

Parallel algorithms for relational coarsest partition problems

Rajasekaran

Lee

1998

IEEE Trans. Parallel Distrib. Syst.

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“…We also use the principal result from [6] in Section 8: PROPOSITION 3.6. Let K be an array of k ≤ n integers between 1 and n. Then K can be stably sorted in O(log(n) log log(n)) time using k/log(n) processors (CRCW).…”

Section: Is An Array Of Processors Some Of Them Marked In a Crcw Mamentioning

confidence: 99%

“…Lemma 3.4 addresses the so-called forward chaining problem [6], in the special case where there are pointer-links between the marked elements. Actually, the same effect can be achieved by a subtle variation of the methods in the above two lemmas, on a CRCW machine, without assuming such links.…”

Section: Lemma 34 With a As Above And Assuming That Each Interval mentioning

confidence: 99%

“…Section 2 introduces the Voronoi diagram together with the convex hull, and proves some facts about "beachlines" and "fringes." Section 3 reviews some parallel operations on arrays, including Valiant's merging technique and some results from [6]. Section 4 introduces the point-location structure definable from a fringe, and Section 5 shows how to use it to locate contour vertices.…”

mentioning

confidence: 99%

“…6 Our technique, like all 7 previous deterministic parallel algorithms, is based on the serial algorithm due to Shamos and Hoey [25]. The set of sites is initially sorted by x-coordinate; then the algorithm proceeds recursively:…”

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confidence: 99%

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A Nearly Optimal Deterministic Parallel Voronoi Diagram Algorithm

Cole¹

1996

Algorithmica

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Abstract.We describe an n-processor, O(log(n) log log(n))-time CRCW algorithm to construct the Voronoi diagram for a set of n point-sites in the plane.Key Words. Voronoi diagram, Parallel algorithm.1. Introduction. Outline of the Algorithm. The Voronoi diagram is a geometric structure of great computational interest: see [5] for a useful survey. This paper addresses the problem of constructing the diagram in parallel, given as input a set of n points ("sites") in the plane. The Voronoi diagram for a set of sites is the locus of points equidistant from two closest sites: Figure 1 illustrates a diagram with 32 sites.The model of parallelism we assume is a CRCW PRAM, a system of independent processors accessing a shared random-access memory, where the same memory cell can be read by several processors simultaneously (concurrent read) and written by several processors simultaneously (concurrent write). Write-conflicts are resolved arbitrarily: the model of computation is an ARBITRARY CRCW PRAM.Each processor is assumed capable of exact rational and integer arithmetic in unit time.Earlier algorithms [1], [9] were presented for CREW 5 machines. The algorithm in [1] used n processors and took O(log 2 (n)) parallel time; that in [2] used n log(n) processors and took O(log(n) log log(n)) parallel time. Our algorithm reduces the overall work (parallel time × number of processors) to O(n log(n) log log(n)), while maintaining a runtime of O(log(n) log log(n)). Both of these figures are within the factor log log(n)

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On Parallel Integer Merging

Berkman¹,

Vishkin²

1993

Information and Computation

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Improved deterministic parallel integer sorting

Cited by 99 publications

References 12 publications

Parallel algorithms for relational coarsest partition problems

Parallel algorithms for relational coarsest partition problems

A Nearly Optimal Deterministic Parallel Voronoi Diagram Algorithm

On Parallel Integer Merging

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