Exploiting a prioritized MAC protocol to efficiently compute interpolations

Consider a network where all nodes share a single broadcast domain such as a wired broadcast network. Nodes take sensor readings but individual sensor readings are not the most important pieces of data in the system. Instead, we are interested in aggregated quantities of the sensor readings such as minimum and maximum values, the number of nodes and the median among a set of sensor readings on different nodes. In this paper we show that a prioritized medium access control (MAC) protocol may advantageously be exploited to efficiently compute aggregated quantities of sensor readings. In this context, we propose a distributed algorithm that has a very low time and message-complexity for computing certain aggregated quantities. Importantly, we show that if every sensor node knows its geographical location, then sensor data can be interpolated with our novel distributed algorithm, and the message-complexity of the algorithm is independent of the number of nodes. Such an interpolation of sensor data can be used to compute any desired function; for example the temperature gradient in a room (e.g., industrial plant) densely populated with sensor nodes, or the gas concentration gradient within a pipeline or traffic tunnel.