Efficiently Answering Top-k Window Aggregate Queries: Calculating Coverage Number Sequences over Hierarchical Structures

Given a set of spatio-temporal objects, a top-k window aggregate query reports top-k tuples that are ordered with respect to the number of objects during a given time interval and within a spatial range. For example, when analyzing traffic density in a city, one wishes to retrieve top-k time intervals in a certain area that are decreasingly ordered according to the number of vehicles passing by. As simply performing sequential scan over all objects is a costly procedure, an index structure is typically built to enhance the query performance. A crucial step during the evaluation is to determine the number of objects in an arbitrary node, called coverage number sequence. This is a challenging task since objects appear and disappear at different time points such that the number of objects in the query node changes over time. Also, as a hierarchical index structure, the value of a node at high level is achieved by performing the aggregation over its child nodes. Simply enumerating all objects rooted in the query node suffers from performance issues mainly due to (i) traversing the sub-tree to retrieve a large number of time points and (ii) repeatedly performing the aggregation at certain time points. We propose an efficient approach to solve the performance issue for both R-tree and Octree and support updating for new arrival data objects being inserted into the index. Our approach outperforms alternative methods in general according to a thorough analysis on the complexity. Coverage number sequences as well as proposed optimization techniques are utilized to enhance the performance of window aggregate queries. We confirm the superiority of our approach over alternative methods by performing a comprehensive experimental evaluation over large real datasets in a database system.