The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...

Bottleneck Steiner tree problem asks to find a Steiner tree for n terminals with at most k Steiner points such that the length of the longest edge in the tree is minimized. The problem has applications in the design of wireless communication networks. In this paper we study a restricted version of the bottleneck Steiner tree problem in the Euclidean plane which requires that only degree-2 Stein...

We present geometric conditions that can be used to restrict or eliminate candidate topologes for Euclidean Steiner minimal trees in , d ≥ 2. Our emphasis is on conditions that are not restricted to the planar case (d = 2). For trees with a Steiner topology we give restrictions on terminal-Steiner connections that are based on the Voronoi diagram associated with the set of terminal nodes. We th...

Let f k (n) denote the maximum of k-subsets of an n-set satisfying the condition in the title. It is proven that f"(n) < f"(n + 1) < with equalities holding iff there exists a Steiner-system Y(t, 2t-1, n). The bounds are approximately best possible for k < 6 and of correct order of magnitude for k > 7, as well, even if the corresponding Steiner-systems do not exist. Exponential lower and upper ...

The Steiner tree problem is a classical, well-studied, NP-hard optimization problem. Here we are given an undirected graph G = (V,E), a subset R of V of terminals, and nonnegative costs ce for all edges e in E. A feasible Steiner tree for a given instance is a tree T in G that spans all terminals in R. The goal is to compute a feasible Steiner tree of smallest cost. In this thesis we will focus...

The notion of Steiner visibility graphs is introduced. Their applicability in connection with the construction of good quality suboptimal solutions to the Euclidean Steiner tree problem with obstacles is discussed. Polynomial algorithms generating Steiner visibility graphs are described.

In this paper we prove the existence of certain Steiner systems. The results of this paper are divided into three sections: In section 1, we investigate Steiner systems of type S(3, 4, 8). In section 2, we study Steiner systems of type S(5, 6, 12), and in the last section we study Steiner systems of type (5, 8, 24), the MOG and the Hexacode. Mathematics Subject Classification: 20C15, 20E28

It is shown that a class of Steiner triple systems of order 2−1, obtained by some special switchings from the Hamming Steiner triple system, is embedded into some perfect code, constructed by known switchings of ijk-components from the binary Hamming code. The number of Steiner triple systems of order n and rank less or equal n− log(n + 1) + 2, embedded into perfect binary codes of length n, is...