On the Bounded-Skew Clock and Steiner Routing Problems

Abstract

We study theminimum-cost bounded-skewrouting 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-skewcase,and for the infinite-skewcase (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-skewplanar routing, and closely approaches the best known performance for the infinite-skewcase. Ourwork provides unifications of the clock routing and Steiner tree heuristic literatures and gives smooth cost-skew tradeoff that enable good engineering solutions.