— An important class of queries over sensor networks are network-wide aggregation queries. In this work we study a class of aggregation queries which we refer to as aggregate threshold queries. The goal of an aggregate threshold query is to continuously monitor the network and give a notification every time an aggregated value crosses a predetermined threshold value. Aggregate threshold queries are of particular importance in a wireless sensor environment, since they allow network-wide events to be detected, with a minimum expenditure of energy. Such network-wide events might include, for example, the variance in sensor readings exceeding a certain threshold. We present an efficient algorithm for implementing arbitrary aggregate threshold queries over sensor networks. Our algorithm is based on a novel geometric approach by which an arbitrary aggregate threshold query can be split into a set of numerical constraints on the readings of the individual sensors. These constraints are us...