Mixed Integer Programming Formulations for Steiner Tree and Quality of Service Multicast Tree Problems

This article presents flow-based mixed integer programming formulations for the Steiner Tree Problem and its variant applied to model and solve the Quality of Service Multicast Tree problem. This is a relevant problem related to nowadays telecommunication networks, particularly Content Delivery Networks, to distribute multimedia over cloud-based Internet systems. To the best of our knowledge, no previous mixed integer programming formulation was proposed for the Quality of Service Multicast Tree problem variant. Experimental evaluation is performed over a set of realistic problem instances from SteinLib, a reference test-set repository, modified accordingly to prove that standard exact solvers are capable of finding solutions to real-world size instances. Exact methods are applied for benchmarking the proposed formulations, finding optimal solutions and low feasible-to-optimal gaps in reasonable execution times.