Flexible aggregate similarity search
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Instant approximate 1-center on road networks via embeddings
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Nearest-neighbor searching under uncertainty
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Fast k-clustering queries on embeddings of road networks
Proceedings of the 3rd International Conference on Computing for Geospatial Research and Applications
Aggregate keyword routing in spatial database
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
Reverse top-k group nearest neighbor search
WAIM'13 Proceedings of the 14th international conference on Web-Age Information Management
Group trip planning queries in spatial databases
SSTD'13 Proceedings of the 13th international conference on Advances in Spatial and Temporal Databases
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Given a set of points P and a query set Q, a group enclosing query (Geq) fetches the point p* â聢聢 P such that the maximum distance of p* to all points in Q is minimized. This problem is equivalent to the Min-Max case (minimizing the maximum distance) of aggregate nearest neighbor queries for spatial databases [27]. This work first designs a new exact solution by exploring new geometric insights, such as the minimum enclosing ball, the convex hull, and the furthest voronoi diagram of the query group. To further reduce the query cost, especially when the dimensionality increases, we turn to approximation algorithms. Our main approximation algorithm has a worst case \sqrt{2}-approximation ratio if one can find the exact nearest neighbor of a point. In practice, its approximation ratio never exceeds 1.05 for a large number of data sets up to six dimensions. We also discuss how to extend it to higher dimensions (up to 74 in our experiment) and show that it still maintains a very good approximation quality (still close to 1) and low query cost. In fixed dimensions, we extend the \sqrt{2}-approximation algorithm to get a (1 + ε)-approximate solution for the Geq problem. Both approximation algorithms have O(\log N + M) query cost in any fixed dimension, where N and M are the sizes of the data set P and query group Q. Extensive experiments on both synthetic and real data sets, up to 10 million points and 74 dimensions, confirm the efficiency, effectiveness, and scalability of the proposed algorithms, especially their significant improvement over the state-of-the-art method.