Efficient Algorithms for the Minimum Shortest Path Steiner . . .

Given an undirected graph G =(V; E) with positive edge weights (lengths) w: E !! + , a set of terminals (sinks) N ` V , and a unique root node r 2 N,ashortest path Steiner arborescence (hereafter an arborescence) is a Steiner tree rooted at r spanning all terminals in N such that every source-tosink path is a shortest path in G. Given a triple (G; N; r), the minimum shortest path Steiner arborescence (MSPSA) problem seeks an arborescence with minimum weight. The MSPSA problem has various applications in the areas of physical design of very large-scale integrated circuits (VLSI), multicast network communication, and supercomputer message routing; various cases have been studied in the literature. In this paper, we propose several heuristics and exact algorithms for the MSPSA problem with applications to VLSI physical design. Experiments indicate that our heuristics generate near optimal results and achieve speedups of orders of magnitude over existing algorithms