Steiner minimal trees in Lp2 Original Research Article

For a finite set of points in a metric space a Steiner Minimal Tree (SMT) is a shortest tree which interconnects these points. We also consider a relative of this problem allowing at most k additional points in the tree (k-SMT), where k is a given number. We intend to discuss these problems for all planes with p-norm, i.e. the affine plane with norm |(t1, t2)|p = (| t1|p + | t2|p)1/p for 1 ⩽ p < ∞ and |(t1 , t2) |∞ = max { | t1 |, | t2|}. We give a survey of results for the combinatorial structure of SMT and k-SMT and show the consequences for the methods to construct such trees.