Massively-dense wireless sensor networks (WSNs) may increase the difficulty of designing efficient and optimal routing algorithms. Since, from a macroscopic perspective, the optimal load-balancing routing problem may be formulated as a set of partial differential equations (PDEs), a scalable routing algorithm may be obtained by using WSNs themselves to solve the PDEs numerically, e.g., through the Gauss–Seidel iteration. To accelerate convergence without sacrificing precision, the proposed distributed Multiplicative Schwarz routing (DMSR) algorithm uses domain decomposition to iteratively solve the PDEs. Furthermore, the precision and parallelism may be improved by adapting an appropriately defined iteration order. Algorithm performance is analyzed theoretically for parallelism and errors, and numerical simulation results are presented to assess the efficiency and effectiveness of DMSR in achieving load balancing.
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