Sobre o problema Euclidiano de Steiner no Rn

Abstract

The Euclidean Steiner Problem (ESP) asks for a network of minimum length interconnecting a finite set of given points in Rn. The distances considered are Euclidean and it’s allowed to add additional points to decrease the overall length of the network. Problems of this nature are often found in several areas of mathematics, engineering, etc. In this work, we study the origins of ESP, their properties, complexity, and resolution methods. We conclude by analyzing a conjecture proposed in 1992 by Warren Smith on the application of this problem to the vertices of an n-dimensional hypercube, which has remained open since its publication.