volume 31, issue 4, P587-611 2004
DOI: 10.1007/s00454-004-2851-2
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## Abstract: This paper is concerned with the Steiner ratio. A number of properties about the structure of the flat sausage and R-Sausage convex polytopes yielding the best Steiner ratio in two-and three-dimensional Euclidean space, and the topology of the Steiner Minimal Tree for the corresponding vertex sets, are presented. OutlineThe most recent survey of the Steiner problem has been conducted by Cieslik. In his work The Steiner ratio he recounts the history of the problem [1]. Cieslik clarifies that the problem is att…

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