Among the properties of homogeneity of incidence structures flagtransitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steiner t-designs (i.e. flag-transitive t-(v, k, 1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially char...

A-Tree is a rectilinear Steiner tree in which every sink is connected to a driver by a shortest length path, while simultaneously minimizing total wire length. This paper presents a polynomial approximation algorithm for the generalized version of A-Tree problem with upper-bounded delays along each path from the driver to the sinks and with restrictions on the number of Steiner nodes. We refer ...

In this paper we study the Steiner tree problem with degree constraints. Motivated by an application in computational biology we first focus on binary Steiner trees in which all node degrees are required to be at most three. We then present results for general degree-constrained Steiner trees. It is shown that finding a binary Steiner is NP-complete for arbitrary graphs. We relate the problem t...

The node-weighted Steiner tree problem is a variation of classical Steiner minimum tree problem. Given a graph G = (V,E) with node weight function C : V → R and a subset X of V , the node-weighted Steiner tree problem is to find a Steiner tree for the set X such that its total weight is minimum. In this paper, we study this problem in unit disk graphs and present a (1+ε)-approximation algorithm...

A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious. La envolvente de las rectas de Wallace-Simson de un triángulo...

Given a set of points, we define a minimum Steiner point tree to be a tree interconnecting these points and possibly some additional points such that the length of every edge is at most 1 and the number of additional points is minimized. We propose using Steiner minimal trees to approximate minimum Steiner point trees. It is shown that in arbitrary metric spaces this gives a performance differe...

Transformations of Steiner tree problem variants have been frequently discussed in the literature. Besides allowing to easily transfer complexity results, they constitute a central pillar of exact state-of-the-art solvers for well-known variants such as the Steiner tree problem in graphs. In this paper transformations for both the prize-collecting Steiner tree problem and the maximum-weight con...

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the ,metric space. In this note, we show that for any Minkowski plane, the Steiner rat...