Unsplittable max-min demand allocation – a routing problem

The end-to-end assignment of bandwidth to node-pairs (demands) in a communication network can be considered fair if it is distributed according to the max-min fair (MMF) principle. This paper investigates the problem of obtaining an MMF allocation if each demand is required to use exactly one path (i.e., to use unsplittable flows). First it is shown that the problem is NP-hard, both if each demand may use an arbitrary path and also if each demand is restricted to use a path from a small, predefined (demand-specific) path-list. Then, a number of mixed integer programming models are presented for the problem. These models constitute a basis for resolution techniques and are therefore examined in terms of computation times on a set of randomly generated problem instances.