Proceedings ArticleDOI
A fast probabilistic parallel sorting algorithm
Rüdiger Reischuk
- pp 212-219
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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Proceedings ArticleDOI
Further applications of random sampling to computational geometry
TL;DR: This paper gives several new demonstrations of the usefulness of random sampling techniques in computational geometry by creating a search structure for arrangements of hyperplanes by sampling the hyperplanes and using information from the resulting arrangement to divide and conquer.
Journal ArticleDOI
Parallel linear programming in fixed dimension almost surely in constant time
Noga Alon,Nimrod Megiddo +1 more
TL;DR: For any fixed dimension d, thelinear programming problem with n quality constraints can be solved on a probabilistic CRCW PRAM with OO(n)processors almost surely in constant time.
Thinking in Parallel: Some Basic Data-Parallel Algorithms and Techniques
TL;DR: These class notes reflect the theorertical part in the Parallel Algorithms course at UMD and the parallel programming part and its computer architecture context within the PRAM-On-Chip Explicit Multi-Threading (XMT) platform is provided through the XMT home page.
Proceedings ArticleDOI
Parallel algorithms for select and partition with noisy comparisons
TL;DR: In this article, the authors consider the problem of finding the kth highest element in a totally ordered set of n elements and partitioning a set into the top k and bottom n − k elements using pairwise comparisons.
Proceedings ArticleDOI
Parallel linear programming in fixed dimension almost surely in constant time
Noga Alon,Nimrod Megiddo +1 more
TL;DR: It is shown that, for any fixed dimension d, the linear programming problem with n inequality constraints can be solvent on a probabilistic CRCW PRAM with O(n) processors almost surely in constant time.
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.