In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P . Path P is allowed to repeat vertices and edges. We call each path in X an exception, and our desired path a shortest exception avoiding path. We formulate a new ver...

We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms tropical geometry. Applications include shortest paths traffic networks with variable link travel times.