Showing papers on "Parallel algorithm published in 1976"
03 May 1976
TL;DR: Parallel programs are presented that determine the transitive closure of a matrix using n 3 processors and connected components of an undirected graph using n 2 processors and in both cases the desired results are obtained in time 0(log2 n).
Abstract: Parallel programs are presented that determine the transitive closure of a matrix using n3 processors and connected components of an undirected graph using n2 processors. In both cases, the desired results are obtained in time 0(log2n). It is assumed that the processors have access to common memory. Simultaneous access to the same location is permitted for fetch, but not store, instructions.The problem of determining the connected components of a graph using a parallel computer has recently appeared in the literature [1,2]. The result in [1] is based on finding the transitive closure of a matrix in time 0(log2n) which can be done using 0(n3) processors. We show that n2 processors are sufficient to solve the connected component problem in time 0(log2n).We present algorithm CLOSURE that will find the transitive closure of Boolean matrix M [n by n] using n3 processors [numbered P(0,0,0) through P(n−1 ,n−1, n−1)] each of which has local memory and each of which can access common array A [n by n].
78 citations
TL;DR: It is proved that a specific algorithm (computer program) achieves the optimal rate of convergence which has been established by the previous papers and is given in a pseudo-Fortran for a hypothetical true parallel computer.
Abstract: This is the third in a sequence of papers on parallel algorithms for adaptive quadrature. The primary aim is to study the rate of convergence achieved by such algorithms. Here we prove that a specific algorithm (computer program) achieves the optimal rate of convergence which has been established by the previous papers. More specifically, under certain reasonable hypotheses, it is proved that this program terminates with a quadrature estimate within the prescribed input accuracy requirement and that this estimate is computed with a number of integrand evaluations of a specified order as the accuracy requirement goes to zero. Since operational parallel computers are still rare, the program is given in a pseudo-Fortran for a hypothetical true (multiple instruction stream, multiple data stream) parallel computer. A simulation shows that this algorithm has a reasonable speed-up, although it is not optimal in this paper.
20 citations
TL;DR: An algorithm for computing the reliability of a reducible network, viz., a network, which can be reduced by series or parallel calculations only, which minimizes computer storage and is fast, therefore it can handle large systems.
Abstract: This paper presents an algorithm for computing the reliability of a reducible network, viz., a network, which can be reduced by series or parallel calculations only. The network is successively reduced. The method minimizes computer storage and is fast, therefore it can handle large systems.
13 citations
TL;DR: A model of parallel computing is presented and six examples illustrate the method of programming and an implementation scheme for programs is presented.
Abstract: This paper presents a model of parallel computing. Six examples illustrate the method of programming. An implementation scheme for programs is also presented.
12 citations