The Steiner ratio of high-dimensional Banach—Minkowski spaces

Authors:
Dietmar Cieslik
Affiliations:
Inst. fur Mathematik und Informatik, University of Greifswald, Johnstr. 15a, Greifswald 17487, Germany
Venue:
Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Year:
2004

Citing 2
Cited 0

A tight bound for the Steiner ratio in Minkowski planes

Discrete Mathematics
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems

Journal of the ACM (JACM)

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Abstract

The Steiner ratio is the greatest lower bound of the ratios of the Steiner Minimal Tree- by the Minimum Spanning Tree-lengths running over all finite subsets of a metric space. We will discuss this quantity for finite-dimensional Banach spaces of high dimension. Particularly, let the quantity Cd defined as the upper bound of the Steiner ratio of all d-dimensional Banach spaces, then limd→∞ Cd = limd→∞ md(B(2)), where md(B(2)) denotes the Steiner ratio of the d-dimensional Euclidean space.