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25th Annual Symposium on Foundations of Computer Science (FOCS 1984)
Singer Island, FL
October 24-October 26
ISBN: 0-8186-0591-X
R.E. Tarjan, AT&T Bell Laboratories
In this paper we propose a new algorithm for finding the blocks (biconnected components) of an undirected graph. A serial implementation runs in 0[n+m] time and space on a graph of n vertices and m edges. A parallel implmentation runs in 0[log n] time and 0[n+m] space using 0[n+m] processors on a concurrent-read, concurrent-write parallel RAM. An alternative implementation runs in 0[n/sup 2/p] time and 0[n/sup 2/] space using any number p /spl les/ n/sup 2/log/sup 2/-n of processors, on a concurrent-read, exclusive-write parallel RAM. The latter algorithm has optimal speedup, assuming an adjacency matrix representation of the input. A general algorithmic technique which simplifies and improve computation of various functions on tress is introduced. This technique typically requires 0(log n) time using 0(n) space on an exclusive-read exclusive-write parallel RAM.
Index Terms:
parallel graph algorithm, biconnected components, blocks, spanning tree
Citation:
R.E. Tarjan, U. Vishkin, "Finding Biconnected Componemts And Computing Tree Functions In Logarithmic Parallel Time," focs, pp.12-20, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984
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