Fast heuristic algorithms for rectilinear steiner trees

A fundamental problem in circuit design is how to connectn points in the plane, to make them electrically common using the least amount of wire. The tree formed, a Steiner tree, is usually constructed with respect to the rectilinear metric. The problem is known to be NP-complete; an extensive review of proposed heuristics is given. An early algorithm by Hanan is shown to have anO(n logn) time implementation using computational geometry techniques. The algorithm can be modified to do sequential searching inO(n ²) total time. However, it is shown that the latter approach runs inO(n ^3/2) expected time, forn points selected from anm×m grid. Empirical results are presented for problems up to 10,000 points.