First Steps Towards Experimental Design in Evaluating Layout Layout Algorithms: Wire Length versus Wire Crossing in Linear Placement Optimization

This report introduces an experimental design that discovers a new relationship between a cell placement for minimized wire crossing in bipartite (two-layer) graphs and a cell placement in linear arrangement, optimized for minimum total wire length as measured after rectilinear routing in a single channel. We introduce hypercrossing, a new crossing model for graphs, and demonstrate that the total wire length in the channel, as measured after routing, has a positive linear correlation with the total hypercrossing, and a coe cient of correlation of near 100%. While heuristics to directly minimize total hypercrossing are yet to be invented, our experiments show that the minimization of total (regular) wire crossing leads to placements with signi cantly reduced wire length and wiring area. A methodology and new datasets are now available to determine, with statistical signi cance, which of the two cost function classes will yield a better placement in general: costs based on the model of the wire length, or costs based on the model of the wire crossing. Our best results to date have been achieved with a wire crossing cost model.