A Threshold-Based Algorithm for Continuous Monitoring of K Nearest Neighbors

Assume a set of moving objects and a central server that monitors their positions over time, while processing continuous nearest neighbor queries from geographically distributed clients. In order to always report up-to-date results, the server could constantly obtain the most recent position of all objects. However, this naive solution requires the transmission of a large number of rapid data streams corresponding to location updates. Intuitively, current information is necessary only for objects that may influence some query result (i.e., they may be included in the nearest neighbor set of some client). Motivated by this observation, we present a threshold-based algorithm for the continuous monitoring of nearest neighbors that minimizes the communication overhead between the server and the data objects. The proposed method can be used with multiple, static, or moving queries, for any distance definition, and does not require additional knowledge (e.g., velocity vectors) besides object locations

Verifying Completeness of Relational Query Answers from Online Servers

10.1145/1330332.1330337ACM Transactions on Information and System Security11

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..

Efficient aggregation over objects with extent

We examine the problem of efficiently computing sum/count/ avg aggregates over objects with non-zero extent. Recent work on computing multi-dimensional aggregates has concentrated on objects with zero extent (points) on a multidimensional grid, or one-dimensional intervals. However, in many spatial and/or spatio-temporal 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 a whole 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 first show that both problems 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. Finally, we introduce the BA-tree 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 reaffirms that the BA-tree has more robust performance. Compared against the augmented R*-tree, the BA-tree offers drastic improvement in query performance at the expense of some limited extra space