Geometric Programming Formulation for Gate Sizing with Pipelining Constraints

We propose a novel framework to solve the combined retiming/gate sizing problem in the context of optimization of acyclic pipelines. The adjustment of sizes to gates in a combinational circuit is a continuous problem, solvable by a variety of convex optimization tools provided the delay model for each gate is placed in a convex framework. Retiming is a discrete problem since it involves physically moving registers from one location to another. In this paper, we enhance an existing convex optimization framework proposed by Boyd et al [1] to handle registers as 0-1 variables. We solve the relaxed formulation as a geometric program and glean valuable information about the circuit's performance. Another significant contribution of our paper is that we show that our problem is NP-hard.