The computation of partial transitive closures is considered as an elementary operation for implementing deductive database systems. A new algorithm supporting this operation is presented. Unlike previously published algorithms, which are based either on matrix-manipulations or on depth-first search strategy, the algorithm presented here uses breadth-first search as its dominant traversal strategy, a graph compression method to minimize temporary results and Tarjan's technique in a new way t o deal with strongly connected components. We show tha t this algorithm is especially suitable for computing partial transitive closures in databases, for i t also aims a t the minimization of disk I/O. Preliminary results of a simulation confirm this suitability. In addition, we present considerations about the implementation.