Length-Bounded and Dynamic k-Splittable Flows

Abstract

Classical network flow problems do not impose restrictions on the choice of paths on which flow is sent. Only the arc capacities of the network have to be obeyed. This scenario is not always realistic. In fact, there are many problems for which, e.g., the number of paths being used to route a commodity or the length of such paths has to be small. These restrictions are considered in the length-bounded k-splittable s-t-flowproblem: The problem is a variant of the well known classical s-t-flow problem with the additional requirement that the number of paths that may be used to route the flow and the maximum length of those paths are bounded. Our main result is that we can efficiently compute a length-bounded s-t-flow which sends one fourth of the maximum flow value while exceeding the length bound by a factor of at most 2. We also show that this result leads to approximation algorithms for dynamic k-splittable s-t-flow