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doi:10.1016/S0166-218X(99)00076-1 
Copyright © 1999 Elsevier Science B.V. All rights reserved.
The Steiner ratio of
Received 10 September 1997;
accepted 23 December 1998.
Available online 18 November 1999.
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Abstract
Let
be the d-dimensional space with 2k-norm. Given a finite set N of points in this space. Find a connected graph G=(V,E) such that N
V and the total length of G is minimal. Such a network is called a Steiner minimal tree (SMT). If we connect pairs of given points only, we find a minimum spanning tree (MST). Whereas an MST is easy to find a method to construct an SMT in
needs exponential time for d=2 and is still unknown for d>2. The Steiner ratio m(d,2k) of
is a measure of how good an MST approximates an SMT. We estimate this quantity.
Author Keywords: Steiner trees; Steiner ratio
Fax: 49-3834-864615; email: cieslik@rz.uni-greifswald.de
