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Book ChapterDOI

Randomization in parallel algorithms and its impact on computational geometry (invited)

29 May 1989-Lecture Notes in Computer Science (Springer Berlin Heidelberg)-Vol. 401, pp 1-8
TL;DR: This paper discusses some of the characteristics of randomized algorithms and also gives applications in computational geometry where use of randomization gives us significant advantage over the best known deterministic parallel algorithms.
Abstract: Randomization offers elegant solutions to some problems in parallel computing. In addition to improved efficiency it often leads to simpler and practical algorithms. In this paper we discuss some of the characteristics of randomized algorithms and also give applications in computational geometry where use of randomization gives us significant advantage over the best known deterministic parallel algorithms.
Citations
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Book
01 Jul 1993
TL;DR: Current issues involved in the development of systems which support ne grain concurrency in a single shared address space are discussed, including algorithmic, architectural, technological, and programming issues.
Abstract: A major challenge for computer science in the 1990s is to determine the extent to which general purpose parallel computing can be achieved. The goal is to deliver both scalable parallel performance and architecture independent parallel software. (Work in the 1980s having shown that either of these alone can be achieved.) Success in this endeavour would permit the long overdue separation of software considerations in parallel computing, from those of hardware. This separation would, in turn, encourage the growth of a large and diverse parallel software industry, and provide a focus for future hardware developments. In recent years a number of new routing and memory management techniques have been developed which permit the eecient implementation of a single shared address space on distributed memory architectures. We also now have a large set of eecient, practical shared memory parallel algorithms for important problems. In this paper we discuss some of the current issues involved in the development of systems which support ne grain concurrency in a single shared address space. The paper covers algorithmic, architectural, technological, and programming issues.

119 citations

References
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Proceedings ArticleDOI
Kenneth L. Clarkson1
06 Jan 1988
TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.
Abstract: Random sampling is used for several new geometric algorithms. The algorithms are “Las Vegas,” and their expected bounds are with respect to the random behavior of the algorithms. One algorithm reports all the intersecting pairs of a set of line segments in the plane, and requires O(A + n log n) expected time, where A is the size of the answer, the number of intersecting pairs reported. The algorithm requires O(n) space in the worst case. Another algorithm computes the convex hull of a point set in E3 in O(n log A) expected time, where n is the number of points and A is the number of points on the surface of the hull. A simple Las Vegas algorithm triangulates simple polygons in O(n log log n) expected time. Algorithms for half-space range reporting are also given. In addition, this paper gives asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets.

1,163 citations

Journal ArticleDOI
TL;DR: There is a distributed randomized algorithm that can route every packet to its destination without two packets passing down the same wire at any one time, and finishes within time $O(\log N)$ with overwhelming probability for all such routing requests.
Abstract: Consider $N = 2^n $ nodes connected by wires to make an n-dimensional binary cube. Suppose that initially the nodes contain one packet each addressed to distinct nodes of the cube. We show that the...

675 citations


"Randomization in parallel algorithm..." refers background or methods in this paper

  • ...For example we have derived an optimal O(logn) time n processors algorithm for constructing the convex hull of points in three dimensions (Reif and Sen[ 18 ])....

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  • ...can be proved that this gives estimates within a constant factor with very high probability (Reif and Sen[ 18 ])....

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Journal ArticleDOI
TL;DR: A uniform distribution a from a uniform distribution on the set 1, 2, 3, 4, 5 is a random number and if a and n are relatively prime, compute the residue varepsilon.
Abstract: Let n be an odd integer. Take a random number a from a uniform distribution on the set $\{1, 2,\cdots, n -1\}$. If a and n are relatively prime, compute the residue $\varepsilon \equiv a^{(n - 1)/2...

593 citations


"Randomization in parallel algorithm..." refers methods in this paper

  • ...Presently the best known deterministic algorithm for this problem takes O(log2n log*n) time using n processors (Dadoun and Kirkpatfick[ 17 ])....

    [...]

Proceedings ArticleDOI
21 Oct 1985
TL;DR: A bottom-up algorithm to handle trees which has two major advantages over the top-down approach: the control structure is straight forward and easier to implement facilitating new algorithms using fewer processors and less time; and problems for which it was too difficult or too complicated to find polylog parallel algorithms are now easy.
Abstract: : Trees play a fundamental role in many computations, both for sequential as well as parallel problems. The classic paradigm applied to generate parallel algorithms in the presence of trees has been divide-conquer; finding a 1/3 - 2/3 separator and recursively solving the two subproblems. A now classic example is Brent's work on parallel evaluation of arithmetic expressions. This top-down approach has several complications, one of which is finding the separators. We define dynamic expression evaluation as the task of evaluating the expression with no free preprocessing. If we apply Brent's method, finding the separators seems to add a factor of log n to the running time. We give a bottom-up algorithm to handle trees. That is, all modifications to the tree are done locally. This bottom-up approach which we call CONTRACT has two major advantages over the top-down approach: (1) the control structure is straight forward and easier to implement facilitating new algorithms using fewer processors and less time; and (2) problems for which it was too difficult or too complicated to find polylog parallel algorithms are now easy.

433 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present efficient parallel algorithms for several basic problems in computational geometry: convex hulls, Voronoi diagrams, detecting line segment intersections, triangulating simple polygons, minimizing a circumscribing triangle, and recursive data-structures for three-dimensional queries.
Abstract: We present efficient parallel algorithms for several basic problems in computational geometry: convex hulls, Voronoi diagrams, detecting line segment intersections, triangulating simple polygons, minimizing a circumscribing triangle, and recursive data-structures for three-dimensional queries.

311 citations