Title: Efficient Algorithms for Optimization of Multicast Networks on the Internet Carlos A.S. Oliveira and Panos M. Pardalos Industrial and Systems Engineering University of Florida oliveira@ufl.edu and pardalos@cao.ise.ufl.edu Abstract: Multicast networking is a type of routing technique that can be used to connect one source of data to multiple destinations. A multicast network implements one or more multicast routing protocols to serve users interested on cooperative applications. The number of such applications have increased steadily in the last few years, incorporating areas such as financial data, software development, virtual conference and multimedia. One of the main problems in this area is the efficient determination of routes from a node in the network to a set of users, also called the {\em multicast group}. A second interesting problem concerns the determination of the minimum number of multicast routers needed to implement the multicast routing, given a set of capacity constraints on the network links. In this talk, we discuss both problems and some of the recent work developed on this area. We present new formulations, and give both approximation as well as heuristic algorithms for the problems above. We also present some computational results of the approaches used.