The power of parallel prefix
TL;DR: This study assumes the weakest PRAM model, where shared memory locations can only be exclusively read or written (the EREW model) to solve the prefix computation problem, when the order of the elements is specified by a linked list.
Abstract: The prefix computation problem is to compute all n initial products a1* . . . *a1,i=1, . . ., n of a set of n elements, where * is an associative operation. An O(((logn) log(2n/p))XI(n/p)) time deterministic parallel algorithm using p≤n processors is presented to solve the prefix computation problem, when the order of the elements is specified by a linked list. For p≤O(n1-e)(e〉0 any constant), this algorithm achieves linear speedup. Such optimal speedup was previously achieved only by probabilistic algorithms. This study assumes the weakest PRAM model, where shared memory locations can only be exclusively read or written (the EREW model).
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TL;DR: It is shown that if t b (n,m) is the parallel time taken for computing a matching in a bipartite graph by a parallel work-optimal algorithm and if there is an algorithm A to compute a maximal match in a general graph in t so (n),m -time then there is a work-Optimal parallel algorithm for finding a maximal matching inA general graph that runs in time O.
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Cites background from "The power of parallel prefix"
...Prefix sums can be found in O (logn) optimal time on an EREW PRAM [9]....
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...Kelsen [8] also describes an O(log2n) time optimal algorithm for computing a fractional matching which is incident with onesixth of the edges of a bipartite graph on an EREW PRAM....
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...In this paper, we use the Parallel Random Access Machine (PRAM) as the model of computation for the parallel algorithms....
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...Prefix sums can be found in O(logn) optimal time on an EREW PRAM [9]....
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...5n) time optimal algorithm Kelsen [8] shows that a matching which is incident with one-sixth of the edges of a bipartite graph can be found in O(log2n) optimal time on an EREW PRAM; thus tb(n,m) = O(log2n)....
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TL;DR: This work considers two limiting cases of this problem when the cardinalities of set A is much greater than that of set B, and presents efficient sequential and parallel algorithms for these two problems.
Abstract: Given a bounding isothetic rectangle BR and two sets of points A and B with cardinalities n and m inside it, we have to find an isothetic rectangle containing maximum number of points from set A and no point from set B. We consider two limiting cases of this problem when the cardinalities of set A (resp. set B) is much greater than that of set B (resp. set ,A). We present efficient sequential and parallel algorithms for these two problems. Our sequential algorithms run in O((n + m)log m + m 2) and O((m+ n) log n + n 2) time respectively. The parallel algorithms in CREW PRAM run in o(log n) ando(log m 2) time using O(max(n,m 2/logm)) and O(max(m,n 2/logn)) processors respectively. Our sequential algorithms are faster than a previous algorithm under these constraints on cardinality. No previous parallel algorithm was known for this problem. We also present an optimal systolic algorithm for the original problem.
1 citations
TL;DR: This algorithm is designed on the basis of WDZ Factorization and parallel prefix algorithm to solve Singularly perturbed boundary value problems and is given for both limited and unlimited processors.
Abstract: In this paper we have given a parallel algorithm to solve Singularly perturbed boundary value problems. This algorithm is designed on the basis of WDZ Factorization and parallel prefix algorithm. We have given the algorithm for both limited and unlimited processors.
1 citations
11 Jul 1989
TL;DR: A number of algorithmic tools have been found useful in the construction of parallel algorithms; among these are prefix computation, ranking, Euler tours, ear decomposition, and matrix calculations.
Abstract: We have described a number of algorithmic tools that have been found useful in the construction of parallel algorithms; among these are prefix computation, ranking, Euler tours, ear decomposition, and matrix calculations. We have also described some of the applications of these tools, and listed many other applications. These algorithms seem likely to be useful not only in their own right, but also as examples of ways to break up other problems into parts suitable for parallel solution.
1 citations
01 Jan 1997
TL;DR: This project investigates the well-known Parallel Random Access Machine (PRAM) model of parallel computation as a practical parallel programming model, and develops a general-purpose PRAM programming language and library, called Fork95, and a library of fundamental, efficiently implemented parallel algorithms and data structures.
Abstract: We investigate the well-known Parallel Random Access Machine (PRAM) model of parallel computation as a practical parallel programming model . The two components of this project are a general-purpose PRAM programming language, called Fork95, and a library, called PAD, of fundamental, efficiently implemented parallel algorithms and data structures. We outline the main features of Fork95 as they apply to the implementation of PAD, and describe the implementation of library procedures for prefix-sums and sorting. The Fork95 compiler generates code for the SB-PRAM, a hardware emulation of the PRAM, which is currently being completed at the University of Saarbrucken. Both language and library can immediately be used with this machine. The project is, however, of independent interest. The programming environment can help the algorithm designer to evaluate the practicality of new parallel algorithms, and can furthermore be used as a tool for teaching and communication of parallel algorithms.
1 citations