Fast, Efficient Parallel Algorithms for Some Graph Problems

Algorithms for solving graph problems on an unbounded parallel model of computation are considered. Parallel algorithms of time complexity $O(\log ^2 n)$ are described for finding biconnected components, bridges, minimum spanning trees and fundamental cycles. In the algorithms for finding minimum spanning trees, bridges, and fundamental cycles, the number of processors used is small enough that the parallel algorithm is efficient in comparison with the best sequential algorithms for these problems. Several other algorithms are presented which are especially suitable for processing sparse graphs.