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.

Difficulty level: Upper Secondary, University