Three physical models for utilizing the area over the cells for routing in standard cell designs are presented. Efficient algorithms for choosing and routing a planar subset of nets over the cells so that the resulting channel density is reduced as much as possible are given. For each of the physical models, it is shown how to arrange intercell routing, over-the-cell routing, and power/ground buses to achieve valid routing solutions. Each algorithm exploits the particular arrangement in the corresponding physical model and produces provably good results in polynomial time. Tests of the algorithms on two industrial standard cell designs show that the method reduces total channel density by as much as 21%.
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