Using structured steiner trees for hierarchical global routing

Abstract

The Steiner problem in a hierarchical graph model, the structured graph, is defined. The problem finds applications to hierarchical global routing. Properties of minimum-cost Steiner trees in structured graphs are investigated. A “top-down” approximate solution to the Steiner problem in structured graphs, called a top-down Steiner tree, is defined, and an algorithm is given to compute such solution. The top-down Steiner tree provides also an approximate solution to the Steiner problem in graphs admitting a structured representation. The properties of such solution are discussed and some experimental results on the quality of the approximation are presented. A reduction in time complexity is demonstrated with respect to both exact and heuristic algorithms applied to such graphs.

Keywords:

• Graphs
• trees
• data structures
• algorithms
• Steiner problem
• VLSI layout
• global routing