PERFORMANCE CONSIDERATIONS ON A RANDOM GRAPH MODEL FOR PARALLEL-PROCESSING

AFRATI, F; STAFYLOPATIS, A

dc.contributor.author	AFRATI, F	en
dc.contributor.author	STAFYLOPATIS, A	en
dc.date.accessioned	2014-03-01T01:09:30Z
dc.date.available	2014-03-01T01:09:30Z
dc.date.issued	1993	en
dc.identifier.issn	0988-3754	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11032
dc.relation.uri	http://www.informatik.uni-trier.de/~ley/db/journals/ita/ita27.html#AfratiS93	en
dc.subject	Parallel Processing	en
dc.subject	Random Graph Model	en
dc.subject.classification	Computer Science, Information Systems	en
dc.title	PERFORMANCE CONSIDERATIONS ON A RANDOM GRAPH MODEL FOR PARALLEL-PROCESSING	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	Consider a random directed acyclic graph (dag) with nodes 1, 2, ..., n, and an edge from node i to node j (only if i >j) with fixed probability p. Such a graph can be thought of as the task graph associated with a job and thus it serves as a parallel processing model; the vertices correspond to tasks and the edges correspond to precedence constraints between tasks. In this case, the length of the graph corresponds to the parallel processing time of the job (an infinite number of available processors is assumed) and the width of the graph corresponds to the parallelism of the job. We estimate here the average length of the random dag (that is, the average processing time of the job) as a function of the probability p and the number of tasks n hy establishing tight lower and upper bounds. The lower (resp. upper) bound is determined as being equal to the average length of a random dag considerably simpler to manipulate than the original one. Furthermore, the asymptotic behaviour of the average length is studied and the results obtained improve previously published results. Finally, asymptotic results are obtained concerning the average width of the task graph; it is shown that the average width tends to 1/p as n --> infinity.	en
heal.publisher	DUNOD	en
heal.journalName	RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS AND APPLICATIONS	en
dc.identifier.isi	ISI:A1993LQ32600007	en
dc.identifier.volume	27	en
dc.identifier.issue	4	en
dc.identifier.spage	367	en
dc.identifier.epage	388	en