Global routing based on Steiner min-max trees

Global routing of multiterminal nets is studied. A novel global router is proposed; each step consists of finding a tree, called a Steiner min-max tree, that is Steiner tree with maximum-weight edge minimized (real vertices represent channels containing terminals of a net, Steiner vertices represent intermediate channels, and weights correspond to densities). An O (min(e loglog e, n/sup 2/)) time algorithm is proposed for obtaining a Steiner min-max tree in a weighted graph with e edges and n vertices. (This result should be contrasted with the NP-completeness of the traditional minimum-length Steiner tree problem). Experimental results on difficult examples, on randomly generated data, on master slice chips, and on benchmark examples from the Physical Design Workshop are included.>