Optimal Nearest Neighbor Queries in Sensor Networks

Abstract

Given a set of $m$ mobile objects in a sensor network, we consider the problem of finding the nearest object among them from any node in the network at any time. These mobile objects are tracked by nearby sensors called proxy nodes. This problem requires an object tracking mechanism which typically relies on two basic operations: query and update. A query is invoked by a node each time when there is a need to find the closest object from it in the network. Updates of an object’s location are initiated when the object moves from one location (proxy node) to another. We present a scalable distributed algorithm for tracking these mobile objects such that both the query cost and the update cost is minimized. The main idea is that given a set of mobile objects our algorithm maintains a virtual tree of downward paths pointing to the objects. Our algorithm guarantees an $\mathcal{O}(1)$ approximation for query cost and an $\mathcal{O}(\min \{\log n,\log D\})$ approximation for update cost in the constant-doubling graph model, where $n$ and $D$, respectively, are the number of nodes and the diameter of the network. We also give polylogarithmic approximations for both query and update cost in the general graph model. Our bounds are deterministic and hold in the worst-case. Moreover, our algorithm requires only polylogarithmic bits of memory per node. To our best knowledge, this is the first algorithm that is asymptotically optimal in handling nearest neighbor queries with low update cost.