A note on efficient aggregate queries in sensor networks

We consider a scenario where nodes in a sensor network hold numeric items, and the task is to evaluate simple functions of the distributed data. In this note we present distributed protocols for computing the median with sublinear space and communication complexity per node. Specifically, we give a deterministic protocol for computing median with polylog complexity and a randomized protocol that computes an approximate median with polyloglog communication complexity per node. On the negative side, we observe that any deterministic protocol that counts the number of distinct data items must have linear complexity in the worst case.