Let ℒd2k 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 ℒd2k needs exponential time for d = 2 and is still unknown for d > 2. The Steiner ratio m(d,2k) of ℒd2k is a measure of how well an MST approximates an SMT. We estimate this quantity.
