A Randomized Parallel Algorithm for Planar Graph Isomorphism

We present a parallel randomized algorithm running on aCRCW PRAM, to determine whether two planar graphs are isomorphic, and if so to find the isomorphism. We assume that we have a tree of separators for each planar graph (which can be computed by known algorithms inO(log2n) time withn1+ϵprocessors,...

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Bibliographic Details
Published in:Journal of algorithms Vol. 28; no. 2; pp. 290 - 314
Main Authors: Gazit, Hillel, Reif, John H
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.08.1998
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
BFS trees
Computer science; control theory; systems
Exact sciences and technology
Graph isomorphism
Information retrieval. Graph
Parallel processing
Planar graphs
Theoretical computing
Parallel processing
BFS trees
Graph isomorphism
Planar graphs
Randomised algorithms
Isomorphic graph
Graph theory
Parallel algorithms
Planar graph
ISSN:0196-6774, 1090-2678
Online Access:Get full text
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Summary:We present a parallel randomized algorithm running on aCRCW PRAM, to determine whether two planar graphs are isomorphic, and if so to find the isomorphism. We assume that we have a tree of separators for each planar graph (which can be computed by known algorithms inO(log2n) time withn1+ϵprocessors, for any ϵ>0). Ifnis the number of vertices, our algorithm takesO(log(n)) time with processors and with a probability of failure of 1/nat most. The algorithm needs 2·log(m)−log(n)+O(log(n)) random bits. The number of random bits can be decreased toO(log(n)) by increasing the number of processors ton3/2+ϵ, for any ϵ>0. Our parallel algorithm has significantly improved processor efficiency, compared to the previous logarithmic time parallel algorithm of Miller and Reif (Siam J. Comput.20(1991), 1128–1147), which requiresn4randomized processors orn5deterministic processors.
ISSN:0196-6774
1090-2678
DOI:10.1006/jagm.1998.0943