An Efficient Parallel Biconnectivity Algorithm

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. A 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 O(n² /p) time and O(n² ) space using any number p n² /log ² n of processors, on a concurrent-read, exclusive-write parallel RAM. The last algorithm has optimal speedup, assuming an adjacency matrix representation of the input. A general algorithmic technique that simplifies and improves computation of various functions on trees is introduced. This technique typically requires O(log n) time using processors and $O(n)$ space on an exclusive-read exclusive-write parallel RAM.