Towards a queueing-based framework for in-network function computation

We seek to develop joint aggregation, routing, and scheduling algorithms that, for any graph topology and a large class of functions, 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, k-th order statistic and range, and for which we can 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 that is shown to be throughput-optimal.