Sorelle Friedler

"A Sensor-Based Framework for Kinetic Data"

We introduce a framework for storing and processing kinetic data observed by sensor networks, such as highway traffic or migratory birds. These sensor networks generate vast quantities of data, which motivates a significant need for data compression. We are given a set of sensors, each of which continuously monitors some region of space. We are interested in the kinetic data generated by a finite set of objects moving through space, as observed by these sensors. Our model relies purely on sensor observations; it allows points to move freely and requires no advance notification of motion plans. Sensor outputs are represented as random processes, where nearby sensors may be statistically dependent. We model the local nature of sensor networks by assuming that two sensor outputs are statistically dependent only if the two sensors are among the k nearest neighbors of each other. We present an algorithm for the lossless compression of the data produced by the network. We show that, under the statistical dependence and locality assumptions of our framework, asymptotically this compression algorithm encodes the data to within a constant factor of the information-theoretic lower bound optimum dictated by the joint entropy of the system.

We also present an efficient algorithm for answering spatio-temporal range queries. Our algorithm operates on a compressed representation of the data, without the need to decompress it. We analyze the efficiency of our algorithm in terms of two natural measures of information content, the statistical and empirical joint entropies of the sensor outputs. We show that with space roughly equal to entropy, queries can be answered in time that is roughly logarithmic in entropy. These results represent the first solution to range searching problems over compressed kinetic sensor data and set the stage for future statistical analysis.

This is joint work with David Mount.