Simple three-layer channel routing algorithms

Abstract

In this paper we present a simple three-layer assignment algorithm for planar layouts generated by a class of layout algorithms. This class of algorithms includes simple variations of the currently best algorithms for the three layer channel routing problem (CRP). More specifically, this class includes algorithms "equivalent" to the following algorithms (i–iii) developed by Mehlhorn, Preparata and Sarrafzadeh [7].

(i) The algorithm that generates planar layouts for the two-terminal net CRP with d _max tracks.

(ii) The algorithm that generates planar layouts for the two- and three-terminal net CRP with at most [3d _max/2] tracks.

(iii) The algorithm that generates planar layouts for the multi-terminal net CRP with at most 2d _max — 1 tracks.

The planar layouts generated by these algorithms and by their "equivalent" algorithms are three-layer wirable by the layer assignment algorithm given in [8]. Our approach is different. We make simple modifications to these layout algorithms and incorporate a simple wire assignment strategy to generate three-layer wirings under the knock-knee model. Consequently, we obtain simpler and faster algorithms that generate three-layer wirings with layouts similar to the ones generated by algorithms (i) – (iii). Our algorithms are faster and conceptually simpler because there is no need to construct diagonal diagrams and legal partitions. The channel width of the wiring generated by our algorithm is identical to that of the corresponding planar layout generated by algorithms (i) – (iii).

This research was supported in part by the National Science Foundation under Grant DCR - 8503163.