From spanners to multipath spanners

This thesis deals with multipath spanners, as an extension of classical graph spanners. A spanner H of a graph G is a spanning subgraph such that for any pair of vertices a, b ∈ V (G) the distance measured in the spanner dH (a, b) isn't too much stretched compared to the distance measured in the original graph dG(a, b). As such there exists a stretch factor (α, β) such that for all a, b ∈ V (G), d_H(a, b) <= α*d_G(a,b)+β. Motivated by multipath routing and after noting that the concept of spanner can be extended to any "non decreasing" metric, we introduce the notion of multipath spanner. After an introduction to the topic, we will show the results obtained. The first part is devoted to edge-disjoint multipath spanners. The second part id devoted to vertex-disjoint spanners.