Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Solving query-retrieval problems by compacting Voronoi diagrams
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Influence sets based on reverse nearest neighbor queries
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
The inverse nearest neighbor problem with astrophysical applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An Index Structure for Efficient Reverse Nearest Neighbor Queries
Proceedings of the 17th International Conference on Data Engineering
C2P: Clustering based on Closest Pairs
Proceedings of the 27th International Conference on Very Large Data Bases
High dimensional reverse nearest neighbor queries
CIKM '03 Proceedings of the twelfth international conference on Information and knowledge management
Reverse Nearest Neighbors in Large Graphs
IEEE Transactions on Knowledge and Data Engineering
Efficient reverse k-nearest neighbor search in arbitrary metric spaces
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Nearest and reverse nearest neighbor queries for moving objects
The VLDB Journal — The International Journal on Very Large Data Bases
Reverse Nearest Neighbor Search in Metric Spaces
IEEE Transactions on Knowledge and Data Engineering
Reverse nearest neighbor aggregates over data streams
VLDB '02 Proceedings of the 28th international conference on Very Large Data Bases
Reverse kNN search in arbitrary dimensionality
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Colored range searching on internal memory
DASFAA'12 Proceedings of the 17th international conference on Database Systems for Advanced Applications - Volume Part II
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Determining the influence of an object on other objects in a database, based on proximity, is important in many applications. Abstractly, we wish to pre-process a set, P, of points in d-space so that the points of P that are assigned a new query point q as a Euclidean nearest neighbor can be reported quickly. These are the reverse nearest neighbors of q and are the ones most influenced by q. This generalizes to bichromatic reverse nearest neighbors, in which two sets, clients and servers, are given, where each client is influenced by some server, and of interest are the clients that are assigned a new server q as a nearest neighbor. Both extend to higher orders k 1, where we seek the points that are assigned q as one of their k nearest neighbors, indicating varying degrees of influence. Each version also has a counterpart where "nearest" is replaced by "farthest", signifying low influence. We present a general approach that solves such reverse proximity query problems in an efficient and unified way, in any dimension, using well-known geometric transformations. We also give simple approximation algorithms in two and three dimensions (the primary domain of GIS applications) that report points that are "close to" being the desired true reverse proximity neighbors, as determined by a user-specified error parameter. This is based on approximating the proximity loci of the points by suitable convex polytopes that are amenable to simple and efficient querying. Theoretical analyses show that our solutions are fast and provably accurate, and this is further confirmed by experiments.