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145
Multidimensional Access Methods
, 1998
"... Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that ..."
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Cited by 561 (3 self)
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Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More
Nearest Neighbor Queries
, 1995
"... A frequently encountered type of query in Geographic Information Systems is to find the k nearest neighbor objects to a given point in space. Processing such queries requires substantially different search algorithms than those for location or range queries. In this paper we present an efficient bra ..."
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Cited by 482 (1 self)
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A frequently encountered type of query in Geographic Information Systems is to find the k nearest neighbor objects to a given point in space. Processing such queries requires substantially different search algorithms than those for location or range queries. In this paper we present an efficient branchandbound Rtree traversal algorithm to find the nearest neighbor object to a point, and then generalize it to finding the k nearest neighbors. We also discuss metrics for an optimistic and a pessimistic search ordering strategy as well as for pruning. Finally, we present the results of several experiments obtained using the implementation of our algorithm and examine the behavior of the metrics and the scalability of the algorithm.
On Packing Rtrees
 In ACM CIKM
, 1993
"... – main idea; file structure – algorithms: insertion/split – deletion – search: range, nn, spatial joins – performance analysis – variations (packed; hilbert;...) 15721 Copyright: C. Faloutsos (2001) 2 Problem • Given a collection of geometric objects (points, lines, polygons,...) • organize them on ..."
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Cited by 220 (16 self)
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– main idea; file structure – algorithms: insertion/split – deletion – search: range, nn, spatial joins – performance analysis – variations (packed; hilbert;...) 15721 Copyright: C. Faloutsos (2001) 2 Problem • Given a collection of geometric objects (points, lines, polygons,...) • organize them on disk, to answer spatial queries (range, nn, etc) 15721 Copyright: C. Faloutsos (2001) 3 1 (Who cares?)
Generalized Search Trees for Database Systems
 IN PROC. 21 ST INTERNATIONAL CONFERENCE ON VLDB
, 1995
"... This paper introduces the Generalized Search Tree (GiST), an index structure supporting an extensible set of queries and data types. The GiST allows new data types to be indexed in a manner supporting queries natural to the types; this is in contrast to previous work on tree extensibility which only ..."
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Cited by 205 (19 self)
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This paper introduces the Generalized Search Tree (GiST), an index structure supporting an extensible set of queries and data types. The GiST allows new data types to be indexed in a manner supporting queries natural to the types; this is in contrast to previous work on tree extensibility which only supported the traditional set of equality and range predicates. In a single data structure, the GiST provides all the basic search tree logic required by a database system, thereby unifying disparate structures such as B+trees and Rtrees in a single piece of code, and opening the application of search trees to general extensibility. To illustrate the exibility of the GiST, we provide simple method implementations that allow it to behave like a B+tree, an Rtree, and an RDtree, a new index for data with setvalued attributes. We also present a preliminary performance analysis of RDtrees, which leads to discussion on the nature of tree indices and how they behave for various datasets.
Selectivity Estimation Without the Attribute Value Independence Assumption
, 1997
"... The result size of a query that involves multiple attributes from the same relation depends on these attributes’joinr data distribution, i.e., the frequencies of all combinations of attribute values. To simplify the estimation of that size, most commercial systems make the artribute value independen ..."
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Cited by 198 (12 self)
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The result size of a query that involves multiple attributes from the same relation depends on these attributes’joinr data distribution, i.e., the frequencies of all combinations of attribute values. To simplify the estimation of that size, most commercial systems make the artribute value independenceassumption and maintain statistics (typically histograms) on individual attributes only. In reality, this assumption is almost always wrong and the resulting estimations tend to be highly inaccurate. In this paper, we propose two main alternatives to effectively approximate (multidimensional) joint data distributions. (a) Using a multidimensional histogram, (b) Using the Singular Value Decomposition (SVD) technique from linear algebra. An extensive set of experiments demonstrates the advantages and disadvantages of the two approaches and the benefits of both compared to the independence assumption. 1
Semantic Data Caching and Replacement
, 1996
"... We propose a semantic model for clientside caching and replacement in a clientserver database system and compare this approach to page caching and tuple caching strategies. Our caching model is based on, and derives its advantages from, three key ideas. First, the client maintains a semantic descr ..."
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Cited by 185 (4 self)
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We propose a semantic model for clientside caching and replacement in a clientserver database system and compare this approach to page caching and tuple caching strategies. Our caching model is based on, and derives its advantages from, three key ideas. First, the client maintains a semantic description of the data in its cache,which allows for a compact specification, as a remainder query, of the tuples needed to answer a query that are not available in the cache. Second, usage information for replacement policies is maintained in an adaptive fashion for semantic regions, which are associated with collections of tuples. This avoids the high overheads of tuple caching and, unlike page caching, is insensitive to bad clustering. Third, maintaining a semantic description of cached data enables the use of sophisticated value functions that incorporate semantic notions of locality, not just LRU or MRU, for cache replacement. We validate these ideas with a detailed performance study that i...
Hilbert Rtree: An improved Rtree using fractals
, 1994
"... We propose a new Rtree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting approach in Rtrees. This is done by proposing an ordering on the Rtree nodes. This ordering has to be 'good', in the sense that it should group 'similar' data rectan ..."
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Cited by 184 (9 self)
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We propose a new Rtree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting approach in Rtrees. This is done by proposing an ordering on the Rtree nodes. This ordering has to be 'good', in the sense that it should group 'similar' data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Following [19] we have chosen the socalled '2Dc' method, which sorts rectangles according to the Hilbert value of the center of the rectangles. Given the ordering, every node has a welldefined set of sibling nodes; thus, we can use deferred splitting. By adjusting the split policy, the Hilbert Rtree can achieve as high utilization as desired. To the contrary, the R tree has no control over the space utilization, typically achieving up to 70%. We designed the manipulation algorithms in detail, and we did a full implementation of the Hilbert Rtree. Our experiments show that the '2to...
Analysis of the clustering properties of the Hilbert spacefilling curve
 IEEE Transactions on Knowledge and Data Engineering
, 2001
"... AbstractÐSeveral schemes for the linear mapping of a multidimensional space have been proposed for various applications, such as access methods for spatiotemporal databases and image compression. In these applications, one of the most desired properties from such linear mappings is clustering, whic ..."
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Cited by 141 (10 self)
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AbstractÐSeveral schemes for the linear mapping of a multidimensional space have been proposed for various applications, such as access methods for spatiotemporal databases and image compression. In these applications, one of the most desired properties from such linear mappings is clustering, which means the locality between objects in the multidimensional space being preserved in the linear space. It is widely believed that the Hilbert spacefilling curve achieves the best clustering [1], [14]. In this paper, we analyze the clustering property of the Hilbert spacefilling curve by deriving closedform formulas for the number of clusters in a given query region of an arbitrary shape (e.g., polygons and polyhedra). Both the asymptotic solution for the general case and the exact solution for a special case generalize previous work [14]. They agree with the empirical results that the number of clusters depends on the hypersurface area of the query region and not on its hypervolume. We also show that the Hilbert curve achieves better clustering than the z curve. From a practical point of view, the formulas given in this paper provide a simple measure that can be used to predict the required disk access behaviors and, hence, the total access time.
MultiStep Processing of Spatial Joins
"... Spatial joins are one of the most importaot operations for combining spatial objects of several relations. IO this paper, spatial join processing is studied in detail for extended spatial objects in twodimensional data space. We present an approach for spatial join processing that is based on three ..."
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Cited by 136 (14 self)
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Spatial joins are one of the most importaot operations for combining spatial objects of several relations. IO this paper, spatial join processing is studied in detail for extended spatial objects in twodimensional data space. We present an approach for spatial join processing that is based on three steps. First, a spatial join is performed on the minimum bounding rectangles of the objects returning a set of candidates. Various approaches for accelerating this step of join processing have been examined at the last year’s conference [BKS 93a]. In this paper, we focus on the problem how to compute the answers from the set of candidates which is handled by the foliowing two steps. First of all, sophisticated approximations are used to identify answers as well as to filter out false hits from the set of candidates. For this purpose, we investigate various types of conservative and progressive approximations. In the last step, the exact geometry of the remaioing candidates has to be tested against the join predicate. The time required for computing spatial joio predicates can essentially be reduced when objects are adequately organized in main memory. IO our approach, objects are fiist decomposed into simple components which are exclusively organized by a mainmemory resident spatial data structure. Overall, we present a complete approach of spatial join processing on complex spatial objects. The performance of the individual steps of our approach is evaluated with data sets from real cartographic applications. The results show that our approach reduces the total execution time of the spatial join by factors.
Efficient organization of large multidimensional arrays
 IN PROC, ELEVENTH INT. CONF. ON DATA ENGINEERING
, 1994
"... Large multidimensional arrays are widely used in scientific and engineering database applications. In this paper, we present methods of organizing arrays to make their access on secondary and tertiary memory devices fast and e cient. We have developed four techniques for doing this: (1) storing the ..."
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Cited by 109 (3 self)
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Large multidimensional arrays are widely used in scientific and engineering database applications. In this paper, we present methods of organizing arrays to make their access on secondary and tertiary memory devices fast and e cient. We have developed four techniques for doing this: (1) storing the array in multidimensional "chunks" to minimize the number of blocks fetched, (2) reordering the chunked array to minimize seek distance between accessed blocks, (3) maintaining redundant copies of the array, each organized for a different chunk size and ordering and (4) partitioning the array onto platters of a tertiary memory device so as to minimize the number of platter switches. Our measurements on real data sets obtained from global change scientists demonstrate that accesses on arrays organized using the above techniques are often an order of magnitude faster than on the original unoptimized data.