Distributed utility maximization for network coding based multicasting: a shortest path approach

Yunnan Wu, Sun-Yuan Kung
2006 IEEE Journal on Selected Areas in Communications  
One central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the net-utility -the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning -is maximized. By employing the MAX of flows characterization of the admissible rate region for multicasting, this paper gives a novel reformulation of the optimization problem that has a separable
more » ... tructure. The Lagrangian relaxation method is applied to decompose the problem into subproblems involving one destination each. Our specific formulation of the primal problem results in two key properties. First, the resulting subproblem after decomposition amounts to the problem of finding a shortest path from the source to each destination. Second, assuming the netutility function is strictly concave, our proposed method enables a near-optimal primal variable to be uniquely recovered from a near-optimal dual variable. A numerical robustness analysis of the primal recovery method is also conducted. For ill-conditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of wellconditioned problems obtained from the original problem by adding quadratic regularization terms. Furthermore, the simulation results confirm the numerical robustness of the proposed algorithms. Finally, the proximal method and the dual subgradient method can be naturally extended to provide an effective solution for applications with multiple multicast sessions.
doi:10.1109/jsac.2006.879356 fatcat:i55sz4ckqfbarpbiy2rvivylwy