Novel Approach to Sub-graph Selection over Coded Wireless Networks with QoS Constraints

In this paper, we study the problem of minimum-cost multicast with network coding, while the maximum end-to-end weight, such as delay, throughput, and security, along paths from the source to each destination is bounded by a constant. We propose a path-based mixed integer programming model for the problem and show that the problem is non-deterministic polynomial (NP)-hard. We apply a column-generation approach to solve this model, where the problem is decomposed into a master linear programming problem and several integer programming sub-problems. We also introduce an approach to get a lower bound of optimal solution. Simulation results demonstrate that using of column-generation approach in combination with network coding to solve this problem can enhance the efficiency of final solution, no matter of the size of underlying network.