SPECIAL PROPERTIES OF THE FERMAT-PROBLEM APPLIED TO LOCAL TOPOLOGY OPTIMIZATION

Abstract

In the field of network planning, local optimization techniques are frequently applied to improve the topology of the network by determining between which nodes a connection should exist. In many cases, some links can be merged at extra nodes (Steiner points) in order to save some costs. Finding these extra points belongs to the weighted Fermat-Weber-problem. In this paper, a new representation and construction of the solution to the Fermat-problem is proposed. General conditions of the technological applicability are presented. Furthermore, upper bounds are given to the achievable cost saving in advance without the construction of the Steiner points.