A general theory of constrained max-min rate allocation for multicast networks

This paper presents a general theory of network maxmin rate assignment as a lexicographic optimization. The model includes multicast and lower bound constraints. The model for multicast allows the sender to send at the maximum rate allowed by the network and the receivers. Equivalent optimality conditions, especially those which can be coded into practical algorithms, are derived. A reference parallel algorithm is also derived. The theoretical results clearly show the important role of the advertised rates in automatable optimality conditions. The theory also shows that, once the single-link problem is solved, the multi-link (network) problem can be simply solved by recursively applying the algorithm for single-link problem.