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Planar-DME: a single-layer zero-skew clock tree router

This paper presents new single-layer, i.e., planar-embeddable, clock tree constructions with exact zero skew under either the linear or the Elmore delay model. Our method, called Planar-DME, consists of two parts. The first algorithm, called Linear-Planar-DME, guarantees an optimal planar zero-skew clock tree (ZST) under the linear delay model. The second algorithm, called Elmore-Planar-DME, uses the Linear-Planar-DME connection topology in constructing a low-cost ZST according to the Elmore delay model. While a planar ZST under the linear delay model is easily converted to a planar ZST under the Elmore model by elongating tree edges in bottom-up order, our key idea is to avoid unneeded wire elongation by iterating the DME construction of ZST and the bottom-up modification of the resulting nonplanar routing. Costs of our planar ZST solutions are comparable to those of the best previous nonplanar ZST solutions, and substantially improve over previous planar clock routing methods.