Equivalence, indicators, quasi-indicators and optimal steiner topologies on four points in space

Abstract

The Steiner tree problem is an intractable optimization problem, which asks for a network, in fact a tree, interconnecting a given point set V in a metric space and minimizing the total length of the network. The tree topology t of the network is called a Steiner topology and a tree T with minimum length with respect to its Steiner topology is called a Steiner tree. As a combinatorial optimization problem, the Steiner tree problem asks for a Steiner tree T with minimum length over all possible topologies t on V. It has been proved that if T is in E3 then the length of T cannot be expressed by radicals even when T spans just 4 points. For such optimization problems in which the objective func..