k-Steiner-minimal-trees in metric spaces

Steiner Minimal Trees ∗

While a spanning tree spans all vertices of a given graph, a Steiner tree spans a given subset of vertices. In the Steiner minimal tree problem, the vertices are divided into two parts: terminals and nonterminal vertices. The terminals are the given vertices which must be included in the solution. The cost of a Steiner tree is defined as the total edge weight. A Steiner tree may contain some no...

Degrees in $k$-minimal label random recursive trees

This article describes the limiting distribution of the degrees of nodes has been derived for a kind of random tree named k-minimal label random recursive tree, as the size of the tree goes to infinity. The outdegree of the tree is equal to the number of customers in a pyramid marketing agency immediatly alluring

Steiner Minimal Trees in Simple Polygons

An O(n log n) time and O(n) space algorithm for the Euclidean Steiner tree problem with four terminals in a simple polygon with n vertices is given. Its applicability to the problem of determining good quality solutions for any number of terminals is discussed.

The Steiner Ratio of Metric Spaces

Full Minimal Steiner Trees on Lattice Sets

Given a finite set of points P in the Euclidean plane, the Steiner problem asks us to constuct a shortest possible network interconnecting P. Such a network is known as a minimal Steiner tree. The Steiner problem is an intrinsically difficult one, having been shown to be NP-hard [7]; however, it often proves far more tractable if we restrict our attention to points in special geometric configur...