25th Annual Symposium onFoundations of Computer Science, 1984. (1984)
Singer Island, FL
Oct. 24, 1984 to Oct. 26, 1984
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.
parallel graph algorithm, biconnected components, blocks, spanning tree
R. Tarjan and U. Vishkin, "Finding Biconnected Componemts And Computing Tree Functions In Logarithmic Parallel Time," 25th Annual Symposium onFoundations of Computer Science, 1984.(FOCS), Singer Island, FL, 1984, pp. 12-20.