On achieving maximum multicast throughput in undirected networks

  • Authors:

  • Zongpeng Li;Baochun Li;Lap Chi Lau

  • Affiliations:

  • Department of Computer Science, University of Calgary, Calgary, AB, Canada;Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada;Department of Computer Science, University of Toronto, Toronto, ON, Canada

  • Venue:
  • IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
  • Year:
  • 2006

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Abstract

The transmission of information within a data network is constrained by the network topology and link capacities. In this paper, we study the fundamental upper bound of information dissemination rates with these constraints in undirected networks, given the unique replicable and encodable properties of information flows. Based on recent advances in network coding and classical modeling techniques in flow networks, we provide a natural linear programming formulation of the maximum multicast rate problem. By applying Lagrangian relaxation on the primal and the dual linear programs (LPs), respectively, we derive a) a necessary and sufficient condition characterizing multicast rate feasibility, and b) an efficient and distributed subgradient algorithm for computing the maximum multicast rate. We also extend our discussions to multiple communication sessions, as well as to overlay and ad hoc network models. Both our theoretical and simulation results conclude that, network coding may not be instrumental to achieve better maximum multicast rates in most cases; rather, it facilitates the design of significantly more efficient algorithms to achieve such optimality.