Distributed Function Calculation over Noisy Networks
Zhidun Zeng, Xin Yang, Ze Zhang, Xiaoyu Mo, Zhiqiang Long · Mathematical Problems in Engineering · 2016
Considering any connected network with unknown initial states for all nodes, the nearest-neighbor rule is utilized for each node to update its own state at every discrete-time step. Distributed function calculation problem is defined for one node to compute some function of the initial values of all the nodes based on its own observations. In this paper, taking into account uncertainties in the network and observations, an algorithm is proposed to compute and explicitly characterize the value of the function in question when the number of successive observations is large enough. While the number of successive observations is not large enough, we provide an approach to obtain the tightest possible bounds on such function by using linear programing optimization techniques. Simulations are provided to demonstrate the theoretical results.