Function Computation over Heterogeneous Wireless Sensor Networks

The problem of function computation in large scale heterogeneous wireless sensor networks (WSNs) is studied. Suppose n sensors are placed in a disk network area with radius n^α, where α is a positive constant. The sensors are located heterogeneously around the sink node, i.e, the density of sensors decreases as the distance from the sink node increases. At one instant, each sensor is assigned an input bit. The target of the sink is to compute a function f of the input bits, where f is either a symmetric or the identity function. Energy-efficient algorithms based on inhomogeneous tessellation of the network are designed and the corresponding optimal energy consumption scaling laws are derived. We show that the proposed algorithms are indeed optimal (except for some polylogarithmic terms) by deriving matching lower bounds on the energy consumption required to compute f. At last, based on the results obtained in this paper as well as those obtained by previous works, some discussions and comparisons are presented. We observe that 1) the heterogeneity extent has a great impact on the computation of both symmetric function and identity function, and 2) the energy usage of computing symmetric function can be significantly smaller than that of computing identity function under certain parameter condition, i.e, performing in-network computation helps save energy.