Efficient CSMA Using Regional Free Energy Approximations

Distributed link scheduling algorithms based on carrier sense multiple access and Gibbs sampling are known to achieve throughput optimality, if certain parameters called the fugacities are appropriately chosen. However, the problem of computing these fugacities is NP-hard. Further, the complexity of the existing stochastic gradient descent-based algorithms that compute the exact fugacities scales exponentially with the network size. In this paper, we propose a general framework to estimate the fugacities using regional free energy approximations. In particular, we derive explicit expressions for approximate fugacities corresponding to any feasible service rate vector. We further prove that our approximate fugacities are exact for the class of chordal graphs. A distinguishing feature of our work is that the regional approximations that we propose are tailored to conflict graphs with small cycles, which is a typical characteristic of wireless networks. Numerical results indicate that the proposed methods are quite accurate, and significantly outperform the existing approximation techniques.