Finding Biconnected Componemts and Computing Tree Functions in Logarithmic Parallel Time

In this paper we propose a new algorithm for finding the blocks (biconnected components) of an undirected graph. A serial implementation runs in O(n+m) time and space on a graph of n vertices and m edges. 4 parallel implementation runs in O(log n) time and O(n+m) space using O(n+m) processors on a concurrent-read, concurrent-write parallel RAM. An alternative implementation runs in Obn2/p3 time and O(n2) space using any number p C n /log 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 improves computation of various functions on trees is introduced. This technique typically requires o(1og n) time using o(n) processors and O(n) space on an exclusive-read exclusive-write parallel RAM.