The Stratified Shortest-Paths Problem (invited paper)

In the last ten years it has become clear that some Internet routing protocols do not compute globally optimal paths, but only locally optimal ones. This represents something rather novel in the context of the vast literature on routing protocols for data networking. This paper introduces the Stratified Shortest-Paths Problem as a tool for exploring the borderline between local and global optimality problems. The paper contains a tutorial overview of the algebraic concepts used.