A probably fast, provably optimal algorithm for rectilinear Steiner trees

Abstract

We use the technique of divide-and-conquer to construct a rectilinear Steiner minimal tree on a set of sites in the plane. A well-known optimal algorithm for this problem by Dreyfus and Wagner [lo] is used to solve the problem in the base case. The run time of our optimal algorithm is probabilistic in nature: for all E > 0, there exists b > 0 such that Prob[T(n) < ] > 1 -E , for n sites uniformly distributed on a rectangle. The key fact in the run-time argument is the existence of probable bounds on the number of edges of an optimal tree crossing our subdivision lines. We can test these bounds in low-degree polynomial time for any given set of sites. 0 1994 John Wiley & Sons, Inc.z b 6 log n

Subexponential Algorithms for Rectilinear Steiner Tree and Arborescence Problems

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Rectilinear Steiner Trees in Narrow Strips

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