On minimal rectilinear Steiner trees in all dimensions

Authors:
Timothy Law Snyder
Affiliations:
-
Venue:
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Year:
1990

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Abstract

It is proved that the length of the longest possible minimum rectilinear Steiner tree of n points in the unit d-cube is asymptotic to &Bgr;dn d-1/d, where &Bgr;d. In addition to replicating Chung and Graham's exact determination of &Bgr;2 = 1, this generalization yields tight new bounds such as 1 ≤ &Bgr;3 4 2.