Primal-dual algorithms for QoS multimedia multicast

The QoS Steiner Tree Problem asks for the most cost-efficient way to multicast multimedia to a heterogeneous collection of users with different consumption rates. We assume that the cost of using a link is not constant but rather depends on the maximum bandwidth routed through the link. Formally, given a graph with costs on the edges, a source node and a set of terminal nodes, each one with a bandwidth requirement, the goal is to find a Steiner tree containing the source, and the cheapest assignment of bandwidth to each of its edges so that each source-to-terminal path in the tree has bandwidth at least as large as the bandwidth required by the terminal. Our main contributions are: (1) new covering-type integer linear program formulations for the problem; (2) two new heuristics based on the primal-dual framework; (3) a primal-dual constant-factor approximation algorithm; (4) an extensive experimental study of the new heuristics and of several previously proposed algorithms.