Nearest Nick Neighbor Roussopoulos Stephen Department College objects to a given requires substantially for location efficient point Park or range in space In this to finding neighbor R tree object the k nearest for an optimistic paper traversaJ to a point neighbors than and a pessimistic an to find and then generalize We also discuss search it ordering our algorithm and examine the scalabfity of the algorithm the behavior of of The efficient queries tion Systems specific the GIS location system database is when and is not objects finding the nearest dow multiple query Another stars which The k furthest nearest familiar even NN with point and objects where to a given more to it query of k nearest if we consider with query or the light years it R trees of the varying win could four bound be is combined remaining Gutt84 Packed R trees access methods subtrees which search algorithm Rous85 Kame94 Beck90 have been primarily range queries and spatial on an for overlap containment efficient branch and processing several experiments on synthetic to demonstrate the performance increases such explores queries for the R trees introduce ordering and pruning the search nearest of it and join queries BKS93 based In this paper we provide 2D range that backtracks R tree variations SRF87 used for overlap containment database search variations when in the away neighbors all to a in the sky could is to find ten it is useful traditional complex technique neighbors of spatial potentially contain NN until no subtree needs be visited In FBF77 a NN algorithm for k d trees was proposed which was later refined in Spro91 request the layout point searches to use a more are at least versatility substantially five unsuccessful by an NN may case of an astrophysics star sizes if we were handled the In the a user NN Informa on the screen situation user spatial involve the Neighbor in Geographic For example to find the of Nearest interest or an object Another is a wide variety algorithm which first goes down the quadtree exploring the subtree that contains the query point in order Then to get a first estimate of the NN location implementation is of a particular There quadtrees The exact k NN problem is also posed for hierarchical spatial data structures such as the PM quadtree The proposed solution is a top down recursive INTRODUCTION 1 movie theaters Same89 However very few have been used for NN In Same90 heuristics are provided to find objects in strategy of the metrics 20742 only metrics as well as for pruning Finally we present the results several experiments obtained using the implementation MD Efficient processing of NN queries requires spatial data structures which capitalize on the proximity of the objects to focus the search of potential neighbors those we present algorithm Vincent Science different such queries queries branch and bound the nearest Processing search algorithms Fr6d6ric other spatial queries such as find the k NN to the East of a location or even spatial joins with NN join predicate such as find the three closest restaurants for each of two of query in Geographic the k nearest neighbor different of Maryland Abstract encountered type Systems is to find Kelley of Computer University A frequently Information Queries exact k NN several metrics for tree and perform and real world data and scalability of our approach To the best of our knowledge neither NN algorithms have been developed for R trees nor similar metrics for NN search We would also like to point out that although the algorithm and these metrics are in as with This research was sponsored partially by the National Science Foundation under grant BIR 9318183 by ARPA under contract 003195 Ve100ID and by NASA USRA under contract 5555 09 the context of R trees all other spatial they are directly applicable to data structures Section 2 of the paper contains the theoretical foundation for the nearest neighbor search Section 3 describes the algorithm and the metrics for ordering the search and pruning during it Section 4 has the experiments with the implementation of the algorithm Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage the ACM copyright notice and the title of the publication and its date appear and notice is given that copyin is by permission of the Association of Computing Machinery o copy otherwise or to republish requires a fee and or specific permission SIGMOD 95 San Jose CA USA Q 1995 ACM 0 89791 731 6 95 0005 3 50 The conclusion 71 is in section 5 NEIGHBOR NEAREST 2 USING R trees trees were in SEARCH R TREES proposed higher as than one a natural extension of dimensions Gutt84 They B combine most of the nice features of both B trees and quadtrees Like B trees they remain balanced while they their maintain the flexibility of dynamically adjusting or dense grouping to deal with either dead space areas like the quad trees do The decomposition used in RECT oid where used as a a pointer an n dimensional which in is an object identifier and to a data object and RECT the a 2 dimensional of the rectangle stored further i e quadrants the next rectangle node entry leaf level are For R tree their atomic spatial contain line c be of the of objects and are primitives segments entries N is corner spatial trapezoids nodes will L I is MBR represents upper right considered n a example RECT composite into triangles p where and possibly decomposed Non leaf RECT an lower left The at the not pixels space Rectangle object z z ig y yhigh which coordinates the Bounding corresponding q M of the form oid Minimal bounds the form cent ain entries LL m k l q R trees is dynamic driven by the spatial data objects And with appropriate split algorithms if a region of an n dimensional space includes dead space no entry in the R tree will be introduced Leaf nodes of the R tree Figure or 1 Collection of Rect angles of the form to a successor node in is a minimal level of the R tree and REC T which bounds all the entries in the descendent The term p is a pointer branching or fan out factor can be used to specify the maximum number of entries that a node can have each node of an R tree with branching factor fifty for example points or leaf objects to a maximum To illustrate of fifty descendants the way an R tree is defined on some space Figure 1 shows a collection of rectangles Performance and Figure 2 the corresponding tree of an R tree search is