An efficient and fast parallel-connected component algorithm

Authors:
Yujie Han;Robert A. Wagner
Affiliations:
Department of Computer Science, University of Kentucky, Lexington, KY and Duke University, Durham, North Carolina;Department of Computer Science, Duke University, Durham, NC
Venue:
Journal of the ACM (JACM)
Year:
1990

Citing 10
Cited 8

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Abstract

A parallel algorithm for computing the connected components of undirected graphs is presented. Shared memory computation models are assumed. For a graph of e edges and n nodes, the time complexity of the algorithm is &Ogr;(e/p + (n log n)/p + log2n) with p processors. The algorithm can be further refined to yield time complexity &Ogr;(H(e, n, p)/p + (n log n)/(p log(n/p)) + log2n), where H(e, n, p) is very close to &Ogr;(e). These results show that linear speedup can be obtained for up to p ≤ e/log2n processors when e ≥ n log n. Linear speedup can still be achieved with up to p ≤ n&egr; processors, 0 ≤ &egr; e ≥ n log(*)n. Our results can be further improved if a more efficient integer sorting algorithm is available.