Clock tree theory

Constructing a zero-skew clock tree can be formulated as constructing a path-length balanced tree (assuming path delay is proportional to path length), i.e., to have identical path length between the root and any leave of the tree. The problem can be in a Euclidean plane, a rectilinear plane, or with other distance metrics. This problem's computation complexity is open. Can you find an approximation algorithm for the problem which guarantees a given error bound?

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