Towards a Queueing-Based Framework for In-Network Function Computation

We seek to develop network algorithms for function computation in sensor networks. Specifically , we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network computation as compared to simple data forwarding. To this end, we define a class of functions, the Fully-Multiplexible functions, which includes several functions such as parity, MAX, and k-th order statistics. For such functions we exactly characterize the maximum achievable refresh rate of the network in terms of an underlying graph primitive, the min-mincut. In wireline networks, we show that the maximum refresh rate is achievable by a simple algorithm that is dynamic, distributed, and only dependent on local information. In the case of wireless networks, we provide a MaxWeight-like algorithm with dynamic flow splitting, which is shown to be throughput-optimal.