On Min-Cost Rectilinear Steiner Distance-Preserving Tree Construction using a Generalized Min-Cost Flow on a Bipartite Network1

Given a signal net N = s; 1; ;n to be the set of nodes, with s the source and the remaining nodes sinks, an MRDPT (minimum-cost rectilinear Steiner distance-preserving tree) has the property that the length of every source to sink path is equal to the rectilinear distance between the source and sink. The minimum-cost rectilinear Steiner distance-preserving tree minimizes the total wire length while maintaining minimal source to sink length. Recently, some heuristic algorithms have been proposed for the problem of nding the MRDPT. In this paper, we investigate an optimal structure on the MRDPT, and present a new graph-theoretic approach which shows that our min-cost ow algorithm built upon a bipartite network transformation leads to an eecient algorithm to identify the MRDPT. A more practical application to VLSI clock designs is also investigated along with interesting open problems.