We show that for every set S of n points in the plane and a designated point rt ∈ S, there exists atree T that has small maximum degree, depth and weight. Moreover, for every point v ∈ S, the distancebetween rt and v in T is within a factor of (1+2) close to their Euclidean distance ‖rt, v‖. We call thesetrees narrow-shallow-low-light (NSLLTs). We demonstrate that our construction a...

Generalized Steiner systems GS(2, 4, v, 2) were first discussed by Etzion and used to construct optimal constant weight codes over an alphabet of size three with minimum Hamming distance five, in which each codeword has length v and weight four. Etzion conjectured its existence for any integer v ≥ 7 and v ≡ 1 (mod 3). The conjecture has been verified for prime powers v > 7 and v ≡ 7 (mod 12) by...

The famous Fermat-Torricelli problem (in Location Science also called the Steiner-Weber problem) asks for the unique point x minimizing the sum of distances to arbitrarily given points x1, . . . ,xn in Euclidean d-dimensional space R. In the present paper, we will consider the extension of this problem to d-dimensional real normed spaces (= Minkowski spaces), where we investigate mainly, but no...

The Steiner k -eccentricity of a vertex v graph G is the maximum distance over all -subsets V ( ) which contain . In this paper 3-eccentricity studied on trees. Some general properties trees are given. A tree transformation does not increase average As its application, several lower and upper bounds for derived.

We analyze the approximation ratio of the average distance heuristic for the Steiner tree problem on graphs, and prove nearly tight bounds for the cases of complete graphs with binary weights f1; dg, or weights in the interval 1; d], where d 2. The improvement over other analyzed algorithms is a factor of about e 2:718.

In this paper we extend the context of Steiner ratio and examine the influence of Steiner points on the weight of a graph in two generalizations of the Euclidean minimum weight connected graph (MST). The studied generalizations are with respect to the weight function and the connectivity condition. First, we consider the Steiner ratio of Euclidean minimum weight connected graph under the budget...

The Steiner distance dc(S) of a subset S of nodes of a connected graph G is the minimum number of edges in a connected subgraph of G that contains S. We consider the behaviour of the expected value ILk (n) of dT(S) and the probability Pk(n, m) that dT(S) rn lover all subsets S of k nodes of trees T of order n from certain families of trees.

With today's development of information technology comes the increased development of numerous real-time multimedia network applications. Some examples include video and tele-conferencing, tele-medicine, video-on-demand, distance education, applications in finance, etc. Several of these applications require multicasting with a certain Quality of Service (QoS). One of the most important QoS para...