A preliminary study of a diagonal channel-routing model

The layout of two-terminal nets in a VLSI channel is realized in a new diagonal channel-routing model (DCRM), where the tracks are segments respectively displayed at +45 ° and –45 ° on the two layers of the channel. A new definition of channel density is introduced, and a lower bound to the channel width is derived by the application of an algorithm, whose complexity is evaluated as a function of the channel density, and other parameters of the problem.A simple linear-time algorithm is proposed, which produces an optimal layout (i.e., it requires a channel of minimum width) if the length of the longest net equals the lower bound for the channel width. In any case, the number of vias is at most one for each net. Some particular solutions are proposed for problems with long nets.Specific problems are much easier in DCRM than in the classical Manhattan model. For example, any shift-by-i can be realized in DCRM in a channel of widthi.This work has been supported by Consiglio Nazionale delle Ricerche of Italy under a research grant.