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 rst algorithm, called Linear-Planar-DME, guarantees an optimal planar zero-skew clock tree (ZST) under the linear delay model. The second algorithm, called ElmorePlanar-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 modi cation of the resulting non-planar routing. Costs of our planar ZST solutions are comparable to those of the best previous non-planar ZST solutions, and substantially improve over previous planar clock routing methods.