N-processors graphs distributively achieve Perfect Matchings in O(log2N) beats

Eli Shamir, Eli Upfal

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

A perfect matching in a graph G(V,E), also called a 1-factor, is a collection P of non-interesting edges engaging (incident with) all the vertices; in case G is bipartite V M @@@@ F, M @@@@ F , P should engage all the vertices of M. The combinatorial problem of finding a perfect matching in G (and its rich ramifications) were extensively studied (and applied) from existential, algorithmic and probabilistic points of view. Here we replace sequential algorithms by distributive, parallel ones. We imagine N processors without a shared memory or a central coordinator (except a clock) reside at the N vertices and communicate by messages. For each particular problem, the edges (giving direct connections) are given and define the input graph G. The collectin of all these graphs is made into a probability space GN (in several ways, as explicated below). In one synchronized Step ( beat), each processor can send a message to a neighbor along an edge of G. One can cheaply implement such steps, uniformly for all graphs, with an efficient switchboard.

Original languageEnglish
Title of host publicationProceedings of the 1st ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 1982
PublisherAssociation for Computing Machinery
Pages238-241
Number of pages4
ISBN (Print)0897910818
DOIs
StatePublished - 18 Aug 1982
Event1st ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 1982 - Ottawa, Canada
Duration: 18 Aug 198220 Aug 1982

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference1st ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 1982
Country/TerritoryCanada
CityOttawa
Period18/08/8220/08/82

Bibliographical note

Publisher Copyright:
© 1982 ACM.

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