Spatio-temporal Range Searching over Compressed Kinetic Sensor Data

Sensor networks and the data they collect have become increasingly prevalent and large. Sensor networks are frequently employed to observe objects in motion and are used to record traffic data, observe wildlife migration patterns, and observe motion from many other settings. In order to perform accurate statistical analyses of this data over arbitrary periods of time, the data must be faithfully recorded and stored. Large sensor networks, for example observing a city’s traffic patterns, may generate gigabytes of data each day. The vast quantities of such data necessitate compression of the sensor observations, yet analysis of these observations is desirable. Ideally, such analysis should operate over the compressed data without decompressing it. Before more sophisticated statistical analyses of the data may be performed, retrieval queries must be supported. In this work, we present the first range searching queries operating over compressed kinetic sensor data. In an earlier paper, we presented an algorithm for losslessly compressing kinetic sensor data and a framework for analyzing its performance. We assume that we are given a set of sensors, which are at fixed locations in a space of constant dimension. (Our results apply generally to metric spaces of constant doubling dimension.) These sensors monitor the movement of a number of kinetic objects. Each sensor monitors an associated region of space, and at regular time steps it records an occupancy count of the number of objects passing through its region. Over time, each sensor produces a string of occupancy counts, and the problem considered previously is how to compress all these strings. Previous compression of sensor data in the literature has focused on stream algorithms and lossy compression of the data. We consider lossless compression. This is often more appropriate in scientific contexts, where analysis is performed after the data has been collected and accurate results are required. Lossless compression algorithms have been studied in the single-string setting, but remain mostly unstudied in a sensor-based setting. In order to query observed sensor data, which ranges over time and space, we need to consider both temporal and spatial queries. Temporal range queries are given a time interval and return an aggregation of the observations over that interval. Spatial range queries are given some region of space (e.g., a rectangle, sphere, or halfplane) and return an aggregation of the observations within that region. Spatio-temporal range queries generalize these by returning an aggregation restricted by both a temporal and a spatial range. We assume that occupancy counts are taken from a commutative semigroup, and the result is a semigroup sum over the range. There are many different