Extending NC and RNC algorithms

A technique is presented by which NC and RNC algorithms for some problems can be extended into NC and RNC algorithms, respectively, that solve more general parametric problems. The technique is demonstrated on explicit bounded degree circuits. Applications include parametric extensions of the shortest-path and spanning-tree problems and, in particular, the minimum-ratio-cycle problem, showing all these problems are in NC. © 1989 Springer-Verlag New York Inc.