Graph Theory and Fibre Optics: A Sample of Current Research

 

Abstract

In this lecture we illustrate how practical problems of algorithm design, motivated by new technologies suggest interesting mathematical questions. These questions may (or may not) be solvable using algorithmic tools. Solutions to such questions may (or may not) be useful for practitioners. Specifically we examine the problem of establishing (multiple) point to point connections in an all-optical network that allows several frequencies to be used in fibres. We seek to minimize the number of frequencies needed to use in such a network. We show that using sets of parallel fibres may allow more efficient solutions. We propose the "Multiple Fibre Conjecture", a graph-theoretic question, that we are able to settle. We sketch the technique used on the solution, and examine the implications of the work for applications. The presentation will be elementary, accessible to non-specialists. (Joint work with Luciano Margara, from the University of Bologna, and IMC Pisa.)