SMe: explicit & implicit constrained-space probabilistic threshold range queries for moving objects

Abstract

This paper studies the constrained-space probabilistic threshold range query (CSPTRQ) for moving objects, where objects move in a constrained-space (i.e., objects are forbidden to be located in some specific areas), and objects' locations are uncertain. We differentiate two forms of CSPTRQs: explicit and implicit ones. Specifically, for each moving object o, we model its location uncertainty as a closed region, u, together with a probability density function. We also model a query range, R, as an arbitrary polygon. An explicit query can be reduced to a search (over all the u) that returns a set of tuples in form of (o, p) such that p ? pt, where p is the probability of o being located in R, and 0≤pt ≤ 1 is a given probabilistic threshold. In contrast, an implicit query returns only a set of objects (without attaching the specific probability information), whose probabilities being located in R are higher than pt. The CSPTRQ is a variant of the traditional probabilistic threshold range query (PTRQ). As objects moving in a constrained-space are common, clearly, it can also find many applications. At the first sight, our problem can be easily tackled by extending existing methods used to answer the PTRQ. Unfortunately, those classical techniques are not well suitable for our problem, due to a set of new challenges. Another method used to answer the constrained-space probabilistic range query (CSPRQ) can be easily extended to tackle our problem, but a simple adaptation of this method is inefficient, due to its weak pruning/validating capability. To solve our problem, we develop targeted solutions that are easy-to-understand and also easy-to-implement. Our central idea is to swap the order of geometric operations and to compute the appearance probability in a multi-step manner. We demonstrate the efficiency and effectiveness of the proposed methods through extensive experiments. Meanwhile, from the experimental results, we further perceive the difference between explicit and implicit queries; this finding is interesting and also meaningful especially for the topics of other types of probabilistic threshold queries.