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

TL;DR

This paper analytically derives the optimal solution for the NP-hard max-min fair multicasting problem, establishing a link with rate balancing, and proposes a low-complexity algorithm validated by simulations.

Contribution

It provides the first analytical solution to the NP-hard MMF multicasting problem and introduces a computationally efficient algorithm based on rate balancing.

Findings

The proposed algorithm outperforms existing methods in simulations.

Rate balancing is equivalent to the optimal MMF solution under certain conditions.

The solution is computationally efficient with closed-form expressions.

Abstract

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.