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The application of retiming and clock skew scheduling for improving the operating speed of synchronous circuits under setup and hold constraints is investigated in this paper. It is shown that when both long and short paths are considered, circuits optimized by the simultaneous application of retiming and clock scheduling can achieve shorter clock periods than optimized circuits generated by applying either of the two techniques separately. A mixed-integer linear programming formulation and an efficient heuristic are given for the problem of simultaneous retiming and clock skew scheduling under setup and hold constraints. Experiments with benchmark circuits demonstrate the efficiency of this heuristic and the effectiveness of the combined optimization. All of the test circuits show improvement. For more than half of them, the maximum operating speed increases by more than 21% over the optimized circuits obtained by applying retiming or clock skew scheduling separately.

Maximizing performance by retiming and clock skew scheduling