NP-Completeness and Approximation Scheme of Zero-Skew Clock Tree Problem

Bao Liu
October 13, 2005

Routing zero skew clock tree with minimum cost is formulated as Path-length Balanced Tree (PBT) problem. Various heuristics have been proposed. The nature of the problem is still open. We prove that PBT problem is NP-complete in Manhattan, Euclidean, and diagonal planes, and present an approximation scheme for path-length delay model with $N^{1+clgN}$ to achieve (1+1/c) OPTIMUM.

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