On the bounded-skew clock and Steiner routing problems

Abstract

We study the minimum-cost bounded-skew routing tree (BST) problem under the linear delay model. This problem captures several engineering tradeoffs in the design of routing topologies with controlled skew. We propose three tradeoff heuristics. (1) For a fixed topology Extended-DME (Ex-DME) extends the DME algorithm for exact zero-skew trees via the concept of a merging region. (2) For arbitrary topology and arbitrary embedding, Extended Greedy-DME (ExG-DME) very closely matches the best known heuristics for the zero-skew case, and for the infinite-skew case (i.e., the Steiner minimal tree problem). (3) For arbitrary topology and single-layer (planar) embedding, the Extended Planar-DME (ExP-DME) algorithm exactly matches the best known heuristic for zero-skew planar routing, and closely approaches the best known performance for the infinite-skew case. Our work provides unifications of the clock routing and Steiner tree heuristic literatures and gives smooth cost-skew tradeoff that enable good engineering solutions.