On the number of minimal 1-Steiner trees

Abstract

We count the number of nonisomorphic geometric minimum spanning trees formed by adding a single point to an n-point set in d-dimensional space, by relating it to a family of convex decompositions of space. The O(nd log2 d 2-d n) bound that we obtain significantly improves previously known bounds and is tight to within a polylogarithmic factor. © 1994 Springer-Verlag New York Inc.