Efficient Aggregation over Objects with Extent

We examine the problem of eciently computing sum/count/avg aggregates over objects with nonzero extent. Recent work on computing multi-dimensional aggregates has concentrated on objects with zero extent (points) on a multi-dimensional grid, or one-dimensional intervals. However, in many spatial and/or spatiotemporal applications objects have extent in various dimensions, while they can be located anywhere in the application space. The aggregation predicate is typically described by a multi-dimensional box (box-sum aggregation). We examine two variations of the problem. In the simple case an object's value contributes to the aggregation result as long as the object intersects the query box. More complex is the functional box-sum aggregation introduced in this paper, where objects participate in the aggregation proportionally to the size of their intersection with the query box. We rst show how the simple and the functional box-sum aggregations can be reduced to dominance-sum queries. Traditionally, dominance-sum queries are addressed in main memory by a static structure, the ECDF-tree. We then propose two extensions, namely, the ECDF-B-trees, that make this structure disk-based and dynamic. The ECDF-B -tree has faster query performance while the ECDF-B -tree has better update. Finally, we introduce the BA-tree, an easily implementable, disk-based and dynamic structure for dominance-sum computation, that combines the advantages from each ECDF-B-tree. We run experiments comparing the performance of the ECDF-B-trees, the BA-tree and a traditional R*-tree (which has been augmented to include aggregation information on its index nodes) over spatial datasets. Our evaluation rearms that the BA-tree has more robust performance than the ECDF-B-trees. More..