Asymptotically efficient retiming under setup and hold constraints

We present a polynomial-time algorithm for retiming synchronous circuits with edge-triggered registers under setup and hold constraints. Given a circuit G and a target clock period c, our algorithm computes in O(V/sup 3/ E) steps a retimed circuit that achieves c and is free of hold violations, where V is the circuit's gate count, and E is the number of wires in the circuit. This is the first polynomial-time algorithm ever reported for retiming with constraints on both long and short paths. The asymptotically efficient operation of our algorithm is based on a novel formulation of the timing constraints as an integer monotonic program with O(E/sup 2/) inequalities.