Minimal Networks - Steiner's Problem (*) Resize


Introduction

The Steiner problem consists of finding the minimal length networks than link a finite number of given points.

One of the applications of this problem is the construction of a network of roads between given cities; if the cost is proportional to the length of the road and if there are no additional constraints, the cheapest network of roads is a minimal network.

Find the Minimal Network that links...

Other situations where considering minimal networks may be of interest are:

the optimization of a network of gas or water pipelines;
the minimization of the length of conducting wires in the construction of electric devices;
the calculation of telephone fares of long distance calls;
in nature, bees instinctively minimize the amount of wax to use to build the beehives (this case concerns areas minimization rather than lengths minimization - the 120º trihedral are minimal networks)
Translated for Atractor by a CMUC team, from its original version in Portuguese. Atractor is grateful for this cooperation.

(*) This web page was done by Isabel Cristina Lopes in the 5th year internship of the Math course at the Science Faculty of the University of Porto.
Since many browsers are blocking Java nowadays, it was decided (in 2021) to convert to Javascript the original applets of this section. This conversion was carried out by a high-school teacher, who is working full-time in Atractor with the support of the Ministry of Education.

Difficulty level: Upper Secondary, University