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Distance Browsing in Spatial Databases
, 1999
"... Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is kn ..."
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Cited by 366 (19 self)
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Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is known prior to the invocation of the algorithm. Thus if m#kneighbors are needed, the knearest neighbor algorithm needs to be reinvoked for m neighbors, thereby possibly performing some redundant computations. The second approach is incremental in the sense that having obtained the k nearest neighbors, the k +1 st neighbor can be obtained without having to calculate the k +1nearest neighbors from scratch. The incremental approach finds use when processing complex queries where one of the conditions involves spatial proximity (e.g., the nearest city to Chicago with population greater than a million), in which case a query engine can make use of a pipelined strategy. A general incremental nearest neighbor algorithm is presented that is applicable to a large class of hierarchical spatial data structures. This algorithm is adapted to the Rtree and its performance is compared to an existing knearest neighbor algorithm for Rtrees [45]. Experiments show that the incremental nearest neighbor algorithm significantly outperforms the knearest neighbor algorithm for distance browsing queries in a spatial database that uses the Rtree as a spatial index. Moreover, the incremental nearest neighbor algorithm also usually outperforms the knearest neighbor algorithm when applied to the knearest neighbor problem for the Rtree, although the improvement is not nearly as large as for distance browsing queries. In fact, we prove informally that, at any step in its execution, the incremental...
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 322 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Ranking in Spatial Databases
, 1995
"... An algorithm for ranking spatial objects according to increasing distance from a query object is introduced and analyzed. The algorithm makes use of a hierarchical spatial data structure. The intended application area is a database environment, where the spatial data structure serves as an index. T ..."
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Cited by 201 (21 self)
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An algorithm for ranking spatial objects according to increasing distance from a query object is introduced and analyzed. The algorithm makes use of a hierarchical spatial data structure. The intended application area is a database environment, where the spatial data structure serves as an index. The algorithm is incremental in the sense that objects are reported one by one, so that a query processor can use the algorithm in a pipelined fashion for complex queries involving proximity. It is well suited for k nearest neighbor queries, and has the property that k needs not be fixed in advance.
Benchmarking Spatial Join Operations with Spatial Output
 Proceedings of the 21st International Conference on Very Large Data Bases
, 1998
"... The spatial join operation is benchmarked using variants of wellknown spatial data structures such as the Rtree, R tree, R + tree, and the PMR quadtree. The focus is on a spatial join with spatial output because the result of the spatial join frequently serves as input to subsequent spatial ..."
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Cited by 32 (8 self)
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The spatial join operation is benchmarked using variants of wellknown spatial data structures such as the Rtree, R tree, R + tree, and the PMR quadtree. The focus is on a spatial join with spatial output because the result of the spatial join frequently serves as input to subsequent spatial operations (i.e., a cascaded spatial join as would be common in a spatial spreadsheet). Thus, in addition to the time required to perform the spatial join itself (whose output is not always required to be spatial), the time to build the spatial data structure also plays an important role in the benchmark. The studied quantities are the time to build the data structure and the time to do the spatial join in an application domain consisting of planar line segment data. Experiments reveal that spatial data structures based on a disjoint decomposition of space and bounding boxes (i.e., the R + tree and the PMR quadtree with bounding boxes) outperform the other structures that are based upon ...
Applications of computational geometry to geographic information systems
 In Handbook of computational geometry
, 2000
"... ..."
Performance of DataParallel Spatial Operations
, 1994
"... The performance of dataparallel algorithms for spatial operations using dataparallel variants of the bucket PMR quadtree, Rtree, and R + tree spatial data structures is compared. The studied operations are data structure build, polygonization, and spatial join in an application domain consisti ..."
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Cited by 23 (6 self)
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The performance of dataparallel algorithms for spatial operations using dataparallel variants of the bucket PMR quadtree, Rtree, and R + tree spatial data structures is compared. The studied operations are data structure build, polygonization, and spatial join in an application domain consisting of planar line segment data (i.e., Bureau of the Census TIGER/Line files). The algorithms are implemented using the scan model of parallel computation on the hypercube architecture of the Connection Machine. The results of experiments reveal that the bucket PMR quadtree outperforms both the Rtree and R + tree. This is primarily because the bucket PMR quadtree yields a regular disjoint decomposition of space while the Rtree and R + tree do not. The regular disjoint decomposition increases the potential for interprocessor communication and parallelism in the bucket PMR quadtree, thereby enabling the execution times to decrease relative to those needed by the Rtree and R + tree. ...
DataParallel Spatial Join Algorithms
, 1994
"... Efficient dataparallel spatial join algorithms for pmr quadtrees and Rtrees, common spatial data structures, are presented. The domain consists of planar line segment data (i.e., Bureau of the Census TIGER/Line files). Parallel algorithms for map intersection and a spatial range query are describe ..."
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Cited by 17 (7 self)
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Efficient dataparallel spatial join algorithms for pmr quadtrees and Rtrees, common spatial data structures, are presented. The domain consists of planar line segment data (i.e., Bureau of the Census TIGER/Line files). Parallel algorithms for map intersection and a spatial range query are described. The algorithms are implemented using the SAM (ScanAndMonotonic mapping) model of parallel computation on the hypercube architecture of the Connection Machine. INTRODUCTION The spatial join is one of the most common operations in spatial databases. This term is usually used in conjunction with a relational database management system [9]. In that context, a join is said to combine entities from two data sets into a single set for every pair of elements in the two sets that satisfy a particular condition. Traditionally, these conditions involve specified attributes that are common to the two sets. In the spatial variant of the join, the condition is usually interpreted as being satisfied...
Hashing by proximity to process duplicates in spatial databases
 In Proceedings of the 3rd International Conference on Information and Knowledge Management (CIKM
, 1994
"... In a spatial database, an object may extend arbitrarily in space. As a result, many spatial data structures (e.g., the quadtree, the cell tree, the R +tree) represent an object by partitioning it into multiple, yet simple, pieces, each of which is stored separately inside the data structure. Many o ..."
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Cited by 12 (7 self)
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In a spatial database, an object may extend arbitrarily in space. As a result, many spatial data structures (e.g., the quadtree, the cell tree, the R +tree) represent an object by partitioning it into multiple, yet simple, pieces, each of which is stored separately inside the data structure. Many operations on these data structures are likely to produce duplicate results because of the multiplicity of object pieces. A novel approach for duplicate processing based on proximity of spatial objects is presented. This is di erent from conventional duplicate elimination in database systems because, with spatial databases, di erent pieces of the same object can span multiple buckets of the underlying data structure. Example algorithms are presented to perform duplicate processing using proximity for a quadtree representation of line segments and arbitrary rectangles. The complexity of the algorithms is seen to depend on a geometric classi cation of di erent instances of the spatial objects. By using proximity and the spatial properties of the objects, the number of diskI/O requests as well as the runtime storage during duplicate processing can be reduced. 1
Decoupling partitioning and grouping: Overcoming shortcomings of spatial indexing with bucketing
 Also University of Maryland Computer Science TR4526
"... The principle of decoupling the partitioning and grouping processes that form the basis of most spatial indexing methods that use tree directories of buckets is explored. The decoupling is designed to overcome the following drawbacks of traditional solutions: (1) multiple postings in disjoint space ..."
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Cited by 4 (3 self)
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The principle of decoupling the partitioning and grouping processes that form the basis of most spatial indexing methods that use tree directories of buckets is explored. The decoupling is designed to overcome the following drawbacks of traditional solutions: (1) multiple postings in disjoint space decomposition methods that lead to balanced trees such as the hBtree where a node split in the event of node overflow may be such that one of the children of the node that was split becomes a child of both of the nodes resulting from the split; (2) multiple coverage and nondisjointness of methods based on object hierarchies such as the Rtree which lead to nonunique search paths; (3) directory nodes with similarlyshaped hyperrectangle bounding boxes with minimum occupancy in disjoint space decomposition methods such as those based on quadtrees and kd trees that make use of regular decomposition. The first two drawbacks are shown to be overcome by the BVtree where as a result of decoupling the partitioning and grouping processes, the union of the regions associated with the nodes at a given level of the directory does not necessarily contain all of the data points although all searches take the same amount of time. The BVtree is not plagued by the third drawback. The third drawback is
Efficient Window Block Retrieval in QuadtreeBased Spatial Databases
 GeoInformatica
, 1996
"... An algorithm is presented to answer window queries in a quadtreebased spatial database environment by retrieving all of the quadtree blocks in the underlying spatial database that cover the quadtree blocks that comprise the window. It works by decomposing the window operation into suboperations ov ..."
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Cited by 4 (2 self)
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An algorithm is presented to answer window queries in a quadtreebased spatial database environment by retrieving all of the quadtree blocks in the underlying spatial database that cover the quadtree blocks that comprise the window. It works by decomposing the window operation into suboperations over smaller window partitions. These partitions are the quadtree blocks corresponding to the window. Although a block b in the underlying spatial database may cover several of the smaller window partitions, b is only retrieved once rather than multiple times. This is achieved by using an auxiliary main memory data structure called the active border which requires O(n) additional storage for a window query of size n \Theta n. As a result, the algorithm generates an optimal number of disk I/O requests to answer a window query (i.e., one request per covering quadtree block). A proof of correctness and an analysis of the algorithm's execution time and space requirements are given, as are some ex...