A linear time algorithm for finding all farthest neighbors in a convex polygon
Information Processing Letters
Computing geodesic furthest neighbors in simple polygons
Journal of Computer and System Sciences
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Distance browsing in spatial databases
ACM Transactions on Database Systems (TODS)
Computing farthest neighbors on a convex polytope
Theoretical Computer Science - Computing and combinatorics
Group Nearest Neighbor Queries
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Aggregate Nearest Neighbor Queries in Road Networks
IEEE Transactions on Knowledge and Data Engineering
Aggregate nearest neighbor queries in spatial databases
ACM Transactions on Database Systems (TODS)
Computer-Aided Design
Probabilistic Group Nearest Neighbor Queries in Uncertain Databases
IEEE Transactions on Knowledge and Data Engineering
Reverse Furthest Neighbors in Spatial Databases
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Incremental Evaluation of Visible Nearest Neighbor Queries
IEEE Transactions on Knowledge and Data Engineering
Group visible nearest neighbor queries in spatial databases
WAIM'10 Proceedings of the 11th international conference on Web-age information management
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In this paper, we study a new type of spatial query, namely aggregate k farthest neighbor (AkFN) search. Given a data point set P, a query point set Q, an AkFN query returns k points in P with the largest aggregate distances to all points in Q. For instance, it is reasonable to build a new hotel where the aggregate distances to all existing hotels are maximized to reduce competition. Our investigation of AkFN queries focuses on three aggregate functions, namely SUM, MAX and MIN. Assuming that the data set is indexed by R-tree, we propose two algorithms, namely minimum bounding (MB) and best first (BF), for efficiently solving AkFN queries with all three aggregate functions. The BF algorithm is incremental and IO optimal. Extensive experiments on both synthetic and real data sets confirm the efficiency and effectiveness of our proposed algorithms.