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217
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 684 (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).
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 594 (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.
FastMap: A Fast Algorithm for Indexing, DataMining and Visualization of Traditional and Multimedia Datasets
, 1995
"... A very promising idea for fast searching in traditional and multimedia databases is to map objects into points in kd space, using k featureextraction functions, provided by a domain expert [25]. Thus, we can subsequently use highly finetuned spatial access methods (SAMs), to answer several types ..."
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Cited by 497 (23 self)
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A very promising idea for fast searching in traditional and multimedia databases is to map objects into points in kd space, using k featureextraction functions, provided by a domain expert [25]. Thus, we can subsequently use highly finetuned spatial access methods (SAMs), to answer several types of queries, including the `Query By Example' type (which translates to a range query); the `all pairs' query (which translates to a spatial join [8]); the nearestneighbor or bestmatch query, etc. However, designing feature extraction functions can be hard. It is relatively easier for a domain expert to assess the similarity/distance of two objects. Given only the distance information though, it is not obvious how to map objects into points. This is exactly the topic of this paper. We describe a fast algorithm to map objects into points in some kdimensional space (k is userdefined), such that the dissimilarities are preserved. There are two benefits from this mapping: (a) efficient ret...
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 390 (20 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...
The TVtree  an index structure for highdimensional data
 VLDB Journal
, 1994
"... We propose a file structure to index highdimensionality data, typically, points in some feature space. The idea is to use only a few of the features, utilizing additional features whenever the additional discriminatory power is absolutely necessary. We present in detail the design of our tree struc ..."
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Cited by 216 (8 self)
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We propose a file structure to index highdimensionality data, typically, points in some feature space. The idea is to use only a few of the features, utilizing additional features whenever the additional discriminatory power is absolutely necessary. We present in detail the design of our tree structure and the associated algorithms that handle such `varying length' feature vectors. Finally we report simulation results, comparing the proposed structure with the R tree, which is one of the most successful methods for lowdimensionality spaces. The results illustrate the superiority of our method, with up to 80% savings in disk accesses. Type of Contribution: New Index Structure, for highdimensionality feature spaces. Algorithms and performance measurements. Keywords: Spatial Index, Similarity Retrieval, Query by Content 1 Introduction Many applications require enhanced indexing, capable of performing similarity searching on several, nontraditional (`exotic') data types. The targ...
A Model for the Prediction of Rtree Performance
, 1996
"... In this paper we present an analytical model that predicts the performance of Rtrees (and its variants) when a range query needs to be answered. The cost model uses knowledge of the dataset only, i.e., the proposed formula that estimates the number of disk accesses is a function of data properties ..."
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Cited by 170 (21 self)
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In this paper we present an analytical model that predicts the performance of Rtrees (and its variants) when a range query needs to be answered. The cost model uses knowledge of the dataset only, i.e., the proposed formula that estimates the number of disk accesses is a function of data properties, namely, the amount of data and their density in the work space. In other words, the proposed model is applicable even before the construction of the Rtree index, a fact that makes it a useful tool for dynamic spatial databases. Several experiments on synthetic and real datasets show that the proposed analytical model is very accurate, the relative error being usually around 10%15%, for uniform and nonuniform distributions. We believe that this error is involved with the gap between efficient Rtree variants, like the R*tree, and an optimum, not implemented yet, method. Our work extends previous research concerning Rtree analysis and constitutes a useful tool for spatial query optimiz...
What is the Nearest Neighbor in High Dimensional Spaces?
, 2000
"... Nearest neighbor search in high dimensional spaces is an interesting and important problem which is relevant for a wide variety of novel database applications. As recent results show, however, the problem is a very difficult one, not only with regards to the performance issue but also to the quality ..."
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Cited by 135 (10 self)
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Nearest neighbor search in high dimensional spaces is an interesting and important problem which is relevant for a wide variety of novel database applications. As recent results show, however, the problem is a very difficult one, not only with regards to the performance issue but also to the quality issue. In this paper, we discuss the quality issue and identify a new generalized notion of nearest neighbor search as the relevant problem in high dimensional space. In contrast to previous approaches, our new notion of nearest neighbor search does not treat all dimensions equally but uses a quality criterion to select relevant dimensions (projections) with respect to the given query. As an example for a useful quality criterion, we rate how well the data is clustered around the query point within the selected projection. We then propose an efficient and effective algorithm to solve the generalized nearest neighbor problem. Our experiments based on a number of real and synthetic data sets show that our new approach provides new insights into the nature of nearest neighbor search on high dimensional data.
Estimating the Selectivity of Spatial Queries Using the `Correlation' Fractal Dimension
, 1995
"... We examine the estimation of selectivities for range and spatial join queries in real spatial databases. As we have shown earlier [FK94a], real point sets: (a) violate consistently the "uniformity" and "independence" assumptions, (b) can often be described as "fractals" ..."
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Cited by 126 (18 self)
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We examine the estimation of selectivities for range and spatial join queries in real spatial databases. As we have shown earlier [FK94a], real point sets: (a) violate consistently the "uniformity" and "independence" assumptions, (b) can often be described as "fractals", with noninteger (fractal) dimension. In this paper we show that, among the infinite family of fractal dimensions, the so called "Correlation Dimension" D 2 is the one that we need to predict the selectivity of spatial join. The main contribution is that, for all the real and synthetic pointsets we tried, the average number of neighbors for a given point of the pointset follows a power law, with D 2 as the exponent. This immediately solves the selectivity estimation for spatial joins, as well as for "biased" range queries (i.e., queries whose centers prefer areas of high point density). We present the formulas to estimate the selectivity for the biased queries, including an integration constant (K `shape 0 ) for ea...
On the Generation of Spatiotemporal Datasets
, 1999
"... . An efficient benchmarking environment for spatiotemporal access methods should at least include modules for generating synthetic datasets, storing datasets (real datasets included), collecting and running access structures, and visualizing experimental results. Focusing on the dataset reposito ..."
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Cited by 116 (12 self)
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. An efficient benchmarking environment for spatiotemporal access methods should at least include modules for generating synthetic datasets, storing datasets (real datasets included), collecting and running access structures, and visualizing experimental results. Focusing on the dataset repository module, a collection of synthetic data that would simulate a variety of real life scenarios is required. Several algorithms have been implemented in the past to generate static spatial (point or rectangular) data, for instance, following a predefined distribution in the workspace. However, by introducing motion, and thus temporal evolution in spatial object definition, generating synthetic data tends to be a complex problem. In this paper, we discuss the parameters to be considered by a generator for such type of data, propose an algorithm, called "Generate_Spatio_Temporal_Data" (GSTD), which generates sets of moving point or rectangular data that follow an extended set of distri...