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For real-time multicast services over wireless multihop networks, to minimize the energy of transmissions with satisfying the requirements of a fixed data rate and high reliabilities, we construct a conflict graph based framework by joint optimizing network coding and scheduling. Then, we propose a primal-dual subgradient optimization algorithm by random sampling K maximal stable sets in a given conflict graph. This method transforms the NP-hard scheduling subproblem into a normal linear programming problem to obtain an approximate solution. The proposed algorithm only needs to adopt centralized technique for solving the linear programming problem while all of the other computations can be distributed. The simulation results show that, comparing with the existing algorithm, this algorithm can not only achieve about 20% performance gain, but also have better performance in terms of convergence and robustness

Minimum-Energy Wireless Real-Time Multicast by Joint Network Coding and Scheduling Optimization