Minimum‐delay routing in continuous‐time dynamic networks with Piecewise‐constant capacities

A single‐source single‐sink dynamic network is considered where the link flows are real‐valued measurable functions defined on a time interval and where storage is allowed at the nodes. Piecewise‐constant link and storage capacities are given. A τ‐maximum flow is a dynamic flow assignment that maximizes the total amount of commodity reaching the sink before time τ. The problem considered is that of computing a flow which is simultaneously τ‐maximum for all τ. Such a flow solves a minimum‐delay dynamic routing problem. An algorithm is presented which computes an optimal flow in O ( | N | 4 T 4 ) time, where | N | is the number of nodes and T is the number of times that the capacities change. Previous polynomial‐time algorithms have been given only for the case of constant capacities.