The power of parallel prefix

Kruskal, Clyde P.; Rudolph, Larry; Snir, Marc

doi:10.1109/tc.1985.6312202

Cited by 206 publications

(63 citation statements)

References 6 publications

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“…Hence, we assume that the intervals in F have been labelled in such a way that b i < b j if and only if i < j. Such a labelling is easily obtained from L in O(log n) time using n/ log n processors by parallel prefixing [14,16]. Let s (respectively, t) be the smallest left endpoint (respectively, largest right endpoint) among those in L. Then, s = a l for some l ∈ {1, 2, .…”

Section: Preliminariesmentioning

confidence: 99%

An improved algorithm for the p-center problem on interval graphs with unit lengths

Cheng

Kang

2007

Computers & Operations Research

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The p-center problem is to locate p facilities in a network of n demand points so as to minimize the longest distance between a demand point and its nearest facility. We consider this problem by modelling the network as an interval graph whose edges all have unit lengths. We present an O(n) time algorithm for the problem under the assumption that the endpoints of the intervals are sorted, which improves on the existing best algorithm for the problem that has a run time of O(pn).

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Section: Preliminariesmentioning

confidence: 99%

An improved algorithm for the p-center problem on interval graphs with unit lengths

Cheng

Kang

2007

Computers & Operations Research

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“…, x k of numbers stored in an array, compute all partial sums r 1 x i . It can be solved with k/log(k) processors (CREW), essentially by covering the array with a balanced tree structure and calculating partial sums of subintervals covered by nodes of the tree [19]. The runtime of log(k) achieved is more or less optimal [23].…”

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

confidence: 99%

“…We call the leaves thus sampled the marked leaves of T . 19 The marked leaves form a subsequence such that between any two leaves in the sequence (in inorder) there are O(k) nodes of T . The span of an internal node v is its set of marked leaf descendants: this is easily calculated from the indexes i and j of the leftmost and rightmost entries in A covering the descendants of v.…”

Section: 10mentioning

confidence: 99%

A nearly optimal deterministic parallel Voronoi diagram algorithm

1996

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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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“…Steps (2) and (3) are performed by using [5] and parallel prefix [16,17]. Steps (4) and (5) are easily handled by using parallel prefix [16,17].…”

Section: For Every Vertexmentioning

confidence: 99%

Optimally Computing the Shortest Weakly Visible Subedge of a Simple Polygon

Chen

1996

Journal of Algorithms

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Given an n-verlex simple polygon P, the problem of computing the shortest weakly visible subedge of P is that of finding a shortest line segment s on the boundary of P such that P is weakly visible from s (if s exists). In this paper, we present new geometric observations that are useful for solving this problem. Based on these geometric observations, we obtain optimal sequential and parallel algorithms for solving this problem. Our sequential algorithm runs in O(n) time, and our parallel algorithm runs in G(logn) time using O(n/ logn) processors in the CREW PRAM computational model. Using the previously best known sequential algorithms to solve this problem would take O(n 2 ) time. We also give geometric observations that lead to extremely simple and optimal algorithms for solving, both sequentially and in parallel, the case of this problem where the polygons are rectilinear.

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The power of parallel prefix

Cited by 206 publications

References 6 publications

An improved algorithm for the p-center problem on interval graphs with unit lengths

An improved algorithm for the p-center problem on interval graphs with unit lengths

A nearly optimal deterministic parallel Voronoi diagram algorithm

Optimally Computing the Shortest Weakly Visible Subedge of a Simple Polygon

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