Estimation of Wirelength Reduction for λ-Geometry vs. Manhattan Placement and Routing

摘要

λ-geometry routing has recently received much attention due to the potential for reduced interconnect length in comparison to today's prevalent Manhattan routing. An accurate cost-benefit analysis of λ-geometry routing is impossible without good estimation of the wirelength reduction expected when switching from Manhattan to λ-geometry routing. However, in the literature, estimates of wirelength improvements achieved by λ-geometry routing are usually for randomly generated nets, and the effect of λ-geometry-driven placement on the overall wirelength improvement is not properly considered. In this paper, we improve existing estimates for the wirelength reduction of various λ-geometry interconnect architectures. First, we give more accurate estimations of the expected wirelength reduction given by λ-geometry routing on Manhattan placements. We take into account the effect of wirelength-driven Manhattan placement on pin locations for nets with k = 2, 3 and 4 pins, and observe smaller expected reductions compared to previous estimates based on nets randomly located in the plane. Second, we estimate the wirelength improvement achieved by λ-geometry placement and routing versus Manhattan placement and routing. Our estimate is based on a simulated annealing placer, driven by λ-geometry metrics. Finally, we discuss and analyze the "virtuous cycle" effect: reduction of overall wirelength results in decreased routing area, which in turn leads to further wirelength reduction.