Algorismes i aplicacions d’aparellaments maximals en grafs

Abstract

[en] The aim of the project is the study of maximal matchings in graphs, both in unweighted graphs and in weighted graphs. For the case of the graphs that are not weighted, we will see how Edmond's algorithm works, which will allows us to find a maximum cardinality matching. After studying the case without weights, we will introduce a few concepts of linear programming in order to be able to solve the weighted case, where we will look for maximum weight matchings. Finally, we will see the applications of these results when finding approximations (one upper bound and one lower bound) in polynomial time for the Travelling Salesman Problem, we will use Christofides’ algorithm to find an upper bound.