Approximate Parallel Scheduling, Vol. 2: Part II: Applications to Optimal Parallel Graph Algorithms in Logarithmic Time (Classic Reprint) - Softcover

Cole, Richard

Softcover

ISBN 10: 1332101542 ISBN 13: 9781332101542

Verlag: Forgotten Books, 2018

Über diesen Titel

Reseña del editor

Excerpt from Approximate Parallel Scheduling, Vol. 2: Part II: Applications to Optimal Parallel Graph Algorithms in Logarithmic Time

To the best of our knowledge, this paper presents for the first time optimal, logarithmic time, parallel algorithms for problems on graphs.

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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Reseña del editor

Excerpt from Approximate Parallel Scheduling, Vol. 2: Part II: Applications to Optimal Parallel Graph Algorithms in Logarithmic Time

Part I of this paper presented a novel technique for approximate parallel scheduling and a new logarithmic time optimal parallel algorithm for the list ranking problem. In this part, we give a new logarithmic time parallel (Pram) algorithm for computing the connected components of undirected graphs which uses this scheduling technique. The connectivity algorithm is optimal unless m= o(n log n), in graphs of n vertices and m edges. Using known results, this new algorithms imply logarithmic time optimal parallel algorithms for a number of other graph problems, including: biconnectivity, Euler tours, strong orientation and r-numbering. Another contribution of the present paper is a parallel union/find algorithm.

To the best of our knowledge, this paper presents for the first time optimal, logarithmic time, parallel algorithms for problems on graphs.

1. Introduction

The models of parallel computation used in this paper are all members of the parallel random, access machine (Pram) family. A Pram employs? synchronous processors all having access to a common memory. An exclusive-read exclusive-write (Crew) Pram does not allow simultaneous access by more than one processor to the same memory location for read or write purposes. A concurrent-read exclusive-write (Crew) Pram allows simultaneous access for reads but not writes. A concurrent-read concurrent-write (Crcw) Pram allows concurrent access for both reads and writes. For the Crcw Pram, we assume that if several processors attempt to write simultaneously at the same memory location then one of them succeeds but we do not know in advance which one. See [Vi-83] for a- survey of results concerning Prams.

Let Seq(n) be the fastest known worst-case running time of a sequential algorithm, where nis the length of the input for the problem at hand. Obviously, the best upper bound on the parallel time achievable using pprocessors, without improving the sequential result, is of the form O(Seqn)/p). A parallel algorithm that achieves this running time is said to have optimal speed-up or more simply to be optimal. A primary goal in parallel computation is to design optimal algorithms that also run as fast as possible.

Most of the problems we consider can be solved by parallel algorithms that obey the following framework.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• ISBN 10: 1332101542
• ISBN 13: 9781332101542
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 52