Joint Routing in Networks

Joint routing of objects through a network consists of nding a set of time-disjoint routes for the objects that maximize the number of objects routed from the source(s) to the sink(s) and minimize the total cost. We show that maximizing the number of objects sent along time-disjoint routes can be modelled as a dynamic network ow problem. We study both this problem and its minimum cost version under several variants and on diierent types of networks, establishing tight bounds on the running time of exact solutions through applications of existing and some new methods.