Distributed Optimisation of MRF-Based Sensor Networks via Dual Decomposition

A major challenge in wireless sensor networks (WSN) is that spatially distributed nodes need to achieve a global task in a completely decentralised manner. Motivated by the fact that optimisation problems in WSNs can often be formulated as Markov random field (MRF) energy minimisation, a general MRF-based framework for the design of distributed WSN algorithms was proposed recently. Building upon this framework and the theory of dual decomposition, we develop a novel WSN optimisation algorithm that is applicable to a wide variety of network problems such as routing and power control. Our algorithm is completely distributed and is characterised by simple, deterministic and identical per-node processing. Routing of control information through the network is avoided as nodes exclusively process information from their local neighbourhoods. We apply our algorithm to a multiple access resource allocation problem and demonstrate rapid convergence to the global optimum.