The Steiner ratio for five points

The Steiner ratio for five points

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Article ID: iaor19921090
Country: Switzerland
Volume: 33
Start Page Number: 419
End Page Number: 436
Publication Date: Nov 1991
Journal: Annals of Operations Research
Authors:
Keywords: Steiner problem
Abstract:

It was conjectured by Gilbert and Pollak that for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least equ1. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees.

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