Optimal non-uniform wire-sizing under the Elmore delay model

We consider non-uniform wire-sizing for general routing trees under the Elmore delay model. Three minimization objectives are studied: (1) total weighted sink-delays; (2) total area subject to sink-delay bounds; and (3) maximum sink delay. We first present an algorithm NWSA-wd for minimizing total weighted sink-delays based on iteratively applying the wire-sizing formula in [1]. We show that NWSA-wd always converges to an optimal wire-sizing solution. Based on NWSA-wd and the Lagrangian relaxation technique, we obtained two algorithms NWSA-db and NWSA-md which can optimally solve the other two minimization objectives. Experimental results show that our algorithms are efficient both in terms of runtime and storage. For example, NWSA-wd, with linear runtime and storage, can solve a 6201-wire segment routing-tree problem using about 1.5-second runtime and 1.3-MB memory on an IBM RS/6000 workstation.