Fast approximation of minimum multicast congestion – implementation versus theory

The problem of minimizing the maximum edge congestion in a multicast communication network generalizes the well-known NP-hard multicommodity flow problem. We give the presently best theoretical approximation results as well as efficient implementations. In particular we show that for a network with m edges and k multicast requests, an r(l + ϵ) (rOPT + exp(1) ln m)-approximation can be computed in O(kmϵ^-2 ln k ln m) time, where β bounds the time for computing an r–approximate minimum Steiner tree. Moreover, we present a new fast heuristic that outperforms the primal-dual approaches with respect to both running time and objective value.