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# A tight lower bound for the Steiner ratio in Minkowski planes

@article{Gao1995ATL, title={A tight lower bound for the Steiner ratio in Minkowski planes}, author={Biao Gao and Dingzhu Du and Ronald L. Graham}, journal={Discrete Mathematics}, year={1995}, volume={142}, pages={49-63} }

- Published 1995 in Discrete Mathematics
DOI:10.1016/0012-365X(95)00005-H

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the metric space. In this note, we show that for any Minkowski plane, the Steiner ratio is at least 2/3. This settles a conjecture of Cieslik (1990) and also Du et al. (1991).

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