CONTRACTION ALGORITHM FOR FINDING SMALL CYCLE-CUTSETS.

We consider the problem of finding a mimimum size vertex set that cuts all directed cycles in a directed graph. Since the general problem is NP-complete we concentrate on finding small cutsets. The algorithm we suggested uses contraction operations to reduce the graph size and to identify candidates for the cutset; the complexity of the algorithm is O( vertical E vertical log vertical V vertical ). Like Shamir-Rosen's algorithm this algorithm guarantees finding a minimum cutset for all reducible flow graphs. Comparison to Shamir-Rosen's algorithm shows that the cutsets produced by our algorithm are 'better'.