Iso-Contour Queries and Gradient Descent with Guaranteed Delivery in Sensor Networks

We study the problem of data-driven routing and navigation in a distributed sensor network over a continuous scalar field. Specifically, we address the problem of searching for the collection of sensors with readings within a specified range. This is named the iso-contour query problem. We develop a gradient based routing scheme such that from any query node, the query message follows the signal field gradient or derived quantities and successfully discovers all iso-contours of interest. Due to the existence of local maxima and minima, the guaranteed delivery requires preprocessing of the signal field and the construction of a contour tree in a distributed fashion. Our approach has the following properties: (i) the gradient routing uses only local node information and its message complexity is close to optimal, as shown by simulations; (ii) the preprocessing message complexity is linear in the number of nodes and the storage requirement for each node is a small constant. The same preprocessing also facilitates route computation between any pair of nodes where the the route lies within any user supplied range of values.