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 rnumbering. 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 exclusiveread exclusivewrite (Crew) Pram does not allow simultaneous access by more than one processor to the same memory location for read or write purposes. A concurrentread exclusivewrite (Crew) Pram allows simultaneous access for reads but not writes. A concurrentread concurrentwrite (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 [Vi83] for a survey of results concerning Prams. Let Seq(n) be the fastest known worstcase 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 speedup 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 stateoftheart 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.
About Richard Cole
Regrettably, currently we cannot provide you with information regarding the actual Manager Richard Cole. But this does not necessarily mean that people do not work on her behalf assortment. We all question which you allow us with this matter. In case you have sparetime and require may profoundly value when you offer you the information. When obtaining these kinds of feedback and knowledge by consumers in regards to the Approximate Parallel Scheduling, Vol. 2 Founder Richard Cole, we 1st the woman's check. Once many of us be sure that most real, just submit this. We see why help and thank you beforehand.Details Book
Author  :  Richard Cole 
Publisher  :  Forgotten Books 
Data Published  :  27 September 2015 
ISBN  :  1332101542 
EAN  :  9781332101542 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  52 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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