Proceedings ArticleDOI
A fast probabilistic parallel sorting algorithm
Rüdiger Reischuk
- pp 212-219
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TLDR
A probabilistic parallel algorithm to sort n keys drawn from some arbitrary total ordered set such that the average runtime is bounded by O(log n), which means the product of time and number of processors meets the information theoretic lower bound for sorting.Abstract:
We describe a probabilistic parallel algorithm to sort n keys drawn from some arbitrary total ordered set. This algorithm can be implemented on a parallel computer consisting of n RAMs, each with small private memory, and a common memory of size O(n) such that the average runtime is bounded by O(log n). Hence for this algorithm the product of time and number of processors meets the information theoretic lower bound for sorting.read more
Citations
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Journal ArticleDOI
On randomization in sequential and distributed algorithms
TL;DR: This survey presents five techniques that have been widely used in the design of randomized algorithms, illustrated using 12 randomized algorithms that span a wide range of applications, including:primality testing, interactive probabilistic proof systems, dining philosophers, and Byzantine agreement.
Proceedings ArticleDOI
Polling: a new randomized sampling technique for computational geometry
John H. Reif,Sandeep Sen +1 more
TL;DR: A new randomized sampling technique, called Polling, is introduced which has applications to deriving efficient parallel algorithms for fundamental problems like the convex hull in three dimensions, Voronoi diagram of point sites on a plane and Euclidean minimal spanning tree.
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Tight Comparison Bounds on the Complexity of Parallel Sorting
Yossi Azar,Uzi Vishkin +1 more
TL;DR: To prove the lower bounds, it is shown that to achieve $k \leqq \log n$ parallel time, the authors need $\Omega (n^{{{1 + 1} / k}} )$ processors.
Journal ArticleDOI
Optimal Randomized Parallel Algorithms for Computational Geometry I
H J Reif,Sandeep Sen +1 more
TL;DR: In this paper, the authors present parallel algorithms for 3-D maxima and two-set dominance counting by an application of integer sorting, which have running time of O(logn)$ using $n$ processors, with very high probability.
Posted Content
Parallel Algorithms for Select and Partition with Noisy Comparisons
TL;DR: This work evaluates algorithms based both on their total runtime and the number of interactive rounds in three comparison models: noiseless, erasure, and noisy (where comparisons are correct with probability 1/2 + γ/2 and incorrect otherwise).
References
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Journal ArticleDOI
Parallelism in Comparison Problems
TL;DR: The worst-case time complexity of algorithms for multiprocessor computers with binary comparisons as the basic operations is investigated and the algorithm for finding the maximum is shown to be optimal for all values of k and n.
Journal ArticleDOI
Expected time bounds for selection
Robert W. Floyd,Ronald L. Rivest +1 more
TL;DR: A new selection algorithm is presented which is shown to be very efficient on the average, both theoretically and practically.
Journal ArticleDOI
New Parallel-Sorting Schemes
TL;DR: A family of parallel-sorting algorithms for a multiprocessor system that is enumeration sortings and includes the use of parallel merging to implement count acquisition, matching the performance of Hirschberg's algoithm, which, however, is not free of fetch conflicts.