A Priori Wire Length Estimation

Abstract

This chapter presents an overview of wire length estimation models. Donath’s pioneering hierarchical placement model [Don79] will be described in the second section and its resulting average wire length estimations will be evaluated.

The most important shortcoming in Donath’s method (the too simplistic model for placement optimization) is tackled first and an extension is presented that does take the optimal placement strategy into account. For this, we augment the hierarchical placement model with an occupation probability for the possible interconnections in an architecture. We then apply this occupation probability at each local level. The same occupation probability was found by Davis by using a technique called “conservation of terminals” and the similarities and differences between Davis’ technique and the method presented here are highlighted.

A unified wire length estimation model is proposed and applied for multiterminal nets. It distinguishes between ‘delay-related’ applications that require estimation of source-sink terminal pair lengths and “routing-related” estimations that are concerned primarily with the length of the entire net. Length estimations for these two approaches are provided.

A last section discusses a totally different aspect, the introduction of external nets into the placement model and the length estimation for such nets. Up to now, external net length estimations have not been dealt with in literature on a priori wire length estimations. Yet, estimating the length of external nets is important and a method for such estimations is provided.