On Parallel Integer Merging
Omer Berkman,Uzi Vishkin +1 more
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TLDR
The problem of merging two sorted arrays A = (a1, a2, ..., an1) and B = (b1, b2,..., bn2) is considered and an algorithm that runs in O(log log log s) time using n/log loglog s CREW PRAM processors (optimal speed-up) and O(ns?) space is presented.Abstract:
The problem of merging two sorted arrays A = (a1, a2, ..., an1) and B = (b1, b2, ..., bn2) is considered. For input elements that are drawn from a domain of integers 1...s] we present an algorithm that runs in O(log log log s) time using n/log log log s CREW PRAM processors (optimal speed-up) and O(ns?) space, where n = n1 + n2. For input elements that are drawn from a domain of integers 1...n] we present a second algorithm that runs in O(?(n)) time (where ?(n) is the inverse of Ackermann?s function) using n/?(n) CREW PRAM processors and linear space. This second algorithm is non-uniform; however, it can be made uniform at a price of a certain loss of speed, or by using a CRCW PRAM.read more
Citations
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Proceedings Article
Improved parallel integer sorting without concurrent writing
Susanne Albers,Torben Hagerup +1 more
TL;DR: The algorithm is closer to optimality than all previous algorithms for the stated problem in the stated model, and the third result matches the operation count of the best known sequential algorithm.
Journal ArticleDOI
Improved Parallel Integer Sorting without Concurrent Writing
Susanne Albers,Torben Hagerup +1 more
TL;DR: In this paper, it was shown that integers in the range 1,?n can be sorted in O((logn)2) time with O(n) operations on an EREW PRAM using a nonstandard word length of O(loglognlogm) bits, thereby greatly improving the upper bound on the word length necessary to sort integers with a linear time?processor product.
Proceedings ArticleDOI
Deterministic sampling—a new technique for fast pattern matching
TL;DR: This work considers the string matching problem and proposes a new linear time serial algorithm for string matching that enables to perform the text analysis in O (log*n) time and optimal speed-up on a PRAM.
Journal ArticleDOI
Parallel algorithms for separable permutations
V. Yugandhar,Sanjeev Saxena +1 more
TL;DR: It is shown that on the CREW model the authors can test whether a given permutation of 1,...,n is separable in O(log n) time with n processors and how the space complexity of the existing serial algorithms for the decision problem can be reduced.
Book ChapterDOI
Structural parallel algorithmics
Uzi Vishkin,Uzi Vishkin +1 more
TL;DR: The first half of the paper is a general introduction which emphasizes the central role that the PRAM model of parallel computation plays in algorithmic studies for parallel computers.
References
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Journal ArticleDOI
Routing, merging, and sorting on parallel models of computation
Allan Borodin,John E. Hopcroft +1 more
TL;DR: Within a spectrum of shared memory models, it is shown that loglog n is asymptotically optimal for n processors to merge two sorted lists containing n elements.