2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1984)

Singer Island, FL

Oct. 24, 1984 to Oct. 26, 1984

ISBN: 0-8186-0591-X

pp: 12-20

R.E. Tarjan , AT&T Bell Laboratories

ABSTRACT

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",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 12-20, 1984, doi:10.1109/SFCS.1984.715896