On the Optimality of Rate Balancing for Max-Min Fair Multicasting

The max-min fair (MMF) multicasting problem is known to be NP-hard. In this work, we analytically derive the optimal solution to this NP-hard problem and establish the equivalence between rate balancing and the optimal MMF multicasting solution under certain conditions. Based on this theoretical insight, we propose a low-complexity algorithm for MMF multicasting that yields closed-form solutions. Simulation results validate our analysis and demonstrate that the proposed algorithm outperforms the state-of-the-art methods while being computationally more efficient.