Fast Connected Components Algorithms for the EREW PRAM

We present fast and efficient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM. On a graph with n vertices and m edges, our randomized algorithm runs in O(log n) time using $(m+n^{1+\epsilon})/\lo...

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Bibliographic Details
Published in:SIAM journal on computing Vol. 28; no. 3; pp. 1021 - 1034
Main Authors: Karger, David R., Nisan, Noam, Parnas, Michal
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.1998
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science
Computer science; control theory; systems
Exact sciences and technology
Graph theory
Information retrieval. Graph
Markov processes
Mathematics
Neighborhoods
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Theoretical computing
Parallel algorithm
Random access memory(RAM)
Graph theory
Fast algorithm
Random walk
Deterministic algorithms
ISSN:0097-5397, 1095-7111
Online Access:Get full text
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Summary:We present fast and efficient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM. On a graph with n vertices and m edges, our randomized algorithm runs in O(log n) time using $(m+n^{1+\epsilon})/\log n$ EREW processors (for any fixed $\epsilon > 0$). A variant uses (m+n)/log n processors and runs in O(log n log log n) time. A deterministic version of the algorithm runs in $O(\log^{1.5}n)$ time using m+n EREW processors.
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ISSN:0097-5397
1095-7111
DOI:10.1137/S009753979325247X