Efficient via shifting algorithms in channel compaction

Abstract

Considers in this paper the problem of shifting vias to obtain more compactable channel routing solutions. Let S be a grid-based two-layer channel routing solution. Let v/sub c/, w/sub c/ be the number of grid points on column c that are occupied by vias, horizontal wires in S, respectively. The authors define the expected height of columns c in S to be h/sub c/=Av/sub c/+Bw/sub c/+C, where A, B, C are some design rule dependent constants. A column in S is said to be a critical column if it has maximum expected height among all columns in S. Let H/sub S/=max/sub c/h/sub c/ be the expected height of the critical column(s) of S. H/sub S/ is an estimation of the height of S after compaction. The authors show that the problem of shifting vias to minimize H/sub S/ can be solved optimally in polynomial time. >