EWA: exact wiring-sizing algorithm

The wire sizing problem under inequality Elmore delay constraints is known to be posynomial, hence convex under an exponential variable-transformation. There are formal methods for solving convex programs. In practice heuristics are often applied because they provide good approximations while offering simpler implementation and better efficiency. There are methods for solving related problems, which are comparable to heuristics from efficiency point of view, but they solve a less desirable formulation in terms of the objective function and constraints. In this paper the EWA algorithm is described. It solves the problem of minimizing the wiring area or capacitance of an interconnect tree subject to constraints on the Elmore delay. EWA is simple to implement and its efficiency is comparable to the available heuristics. No restrictions are placed on the circuit or wire widths, e.g., non-monotone wire widths assignment solutions are feasible. We prove that the optimal wire width assignment for a minimum wiring area objective satisfies all the delay constraint as equalities, when minimum wire width constraints are relaxed. It follows that EWA can be applied also for problems with equality delay constraints such as clock trees. This and other described properties are general enough to permit extensions to higher order delay models in the future.