Abstract
We show that anyn-net 2-terminal channel routing problem of densityd can be wired on a two-layer grid of widthw =d +O(d 2/3) when vertical wire segments are allowed to overlap for a distance of length 1. This is a considerable asymptotic improvement over the best known, and optimal, channel width of 2d-1 for models in which no vertical overlap is allowed [RBM, PL]. Our result also improves the 3d/2+O(1) channel width achieved by a recent algorithm [G] for the same vertical overlap model. The algorithm presented in this paper produces at most 4 overlaps of unit length between any two nets, usesO(n) contacts, and can be implemented to run inO(nd 2/3) time. We also generalize the algorithm to multi-terminal channel routing problems for which our algorithm uses a width ofw = 2d +O(d 2/3).
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