Monitoring the Top-m Aggregation in a Sliding Window of Spatial Queries

Abstract

In this paper, we propose and study the problem of top-m rank aggregation of spatial objects in streaming queries, where, given a set of objects O, a stream of spatial queries (kNN or range), the goal is to report m objects with the highest aggregate rank. The rank of an object w.r.t. an individual query is computed based on its distance from the query location, and the aggregate rank is computed from all of the individual rank orderings. Solutions to this fundamental problem can be used to monitor the popularity of spatial objects, which in turn can provide new analytical tools for spatial data. Our work draws inspiration from three different domains: rank aggregation, continuous queries and spatial databases. To the best of our knowledge, there is no prior work that considers all three problem domains in a single context. Our problem is different from the classical rank aggregation problem in the way that the rank of spatial objects are dependent on streaming queries whose locations are not known a priori, and is different from the problem of continuous spatial queries because new query locations can arrive in any region, but do not move. In order to solve this problem, we show how to upper and lower bound the rank of an object for any unseen query. Then we propose an approximation solution to continuously monitor the top-m objects efficiently, for which we design an Inverted Rank File (IRF) index to guarantee the error bound of the solution. In particular, we propose the notion of safe ranking to determine whether the current result is still valid or not when new queries arrive, and propose the notion of validation objects to limit the number of objects to update in the top-m results. We also propose an exact solution for applications where an approximate solution is not sufficient. Last, we conduct extensive experiments to verify the efficiency and effectiveness of our solutions.