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167
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 ..."
Abstract

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
Fast Subsequence Matching in TimeSeries Databases
 SIGMOD 94
, 1994
"... We present an efficient indexing method to locate 1dimensional subsequences witbin a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of multidimensional rectangles in feature space ..."
Abstract

Cited by 430 (21 self)
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We present an efficient indexing method to locate 1dimensional subsequences witbin a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of multidimensional rectangles in feature space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*tree [9]. In more deteil, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an efficient and effective algorithm to divide such trails into subtrails, which are subsequently represented by their Minimum Bounding Rectangles (MBRs). We also examine queries of varying lengths, and we show how to handle each case efficiently. We implemented our method and carried out experiments on synthetic and real data (stock price movements). We compared the method to sequential scanning, which is the only obvious competitor. The results were excellent: our method accelerated the search time from 3 times up to 100 times.
Indexing the Positions of Continuously Moving Objects
, 2000
"... The coming years will witness dramatic advances in wireless communications as well as positioning technologies. As a result, tracking the changing positions of objects capable of continuous movement is becoming increasingly feasible and necessary. The present paper proposes a novel, R # tree base ..."
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Cited by 317 (18 self)
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The coming years will witness dramatic advances in wireless communications as well as positioning technologies. As a result, tracking the changing positions of objects capable of continuous movement is becoming increasingly feasible and necessary. The present paper proposes a novel, R # tree based indexing technique that supports the efficient querying of the current and projected future positions of such moving objects. The technique is capable of indexing objects moving in one, two, and threedimensional space. Update algorithms enable the index to accommodate a dynamic data set, where objects may appear and disappear, and where changes occur in the anticipated positions of existing objects. A comprehensive performance study is reported.
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 291 (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...
Accelerating XPath location steps
 ACM SIGMOD Int. Conference on Management of Data
, 2002
"... This work is a proposal for a database index structure that has been specifically designed to support the evaluation of XPath queries. As such, the index is capable to support all XPath axes (including ancestor, following, precedingsibling, descendantorself, etc.). This feature lets the index stan ..."
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Cited by 211 (18 self)
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This work is a proposal for a database index structure that has been specifically designed to support the evaluation of XPath queries. As such, the index is capable to support all XPath axes (including ancestor, following, precedingsibling, descendantorself, etc.). This feature lets the index stand out among related work on XML indexing structures which had a focus on regular path expressions (which correspond to the XPath axes children and descendantorself plus name tests). Its ability to start traversals from arbitrary context nodes in an XML document additionally enables the index to support the evaluation of path traversals embedded in XQuery expressions. Despite its flexibility, the new index can be implemented and queried using purely relational techniques, but it performs especially well if the underlying database host provides support for Rtrees. A performance assessment which shows quite promising results completes this proposal. 1.
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.
On Indexing Mobile Objects
, 1999
"... We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic ..."
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Cited by 200 (14 self)
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We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic, external memory algorithm with guaranteed worst case performance and linear space and (ii) a practical approximation algorithm also in the dynamic, external memory setting, which has linear space and expected logarithmic query time. We also give an algorithm with guaranteed logarithmic query time for a restricted version of the problem. We present extensions of our techniques to two dimensions. In addition we give a lower bound on the number of I/O's needed to answer the ddimensional problem. Initial experimental results and comparisons to traditional indexing approaches are also included. 1 Introduction Traditional database management systems assume that data stored in the database rem...
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...
Beyond uniformity and independence: Analysis of rtrees using the concept of fractal dimension
 In Proc. PODS
, 1994
"... We propose the concept of fractal dimension of a set of points, in order to quantify the deviation from the uniformity distribution. Using measurements on real data sets (road intersections of U.S. counties, star coordinates from NASA’s InfraredUltraviolet Explorer etc.) we provide evidence that re ..."
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Cited by 154 (19 self)
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We propose the concept of fractal dimension of a set of points, in order to quantify the deviation from the uniformity distribution. Using measurements on real data sets (road intersections of U.S. counties, star coordinates from NASA’s InfraredUltraviolet Explorer etc.) we provide evidence that real data indeed are skewed, and, moreover, we show that they behave as mathematical fractals, with a measurable, noninteger fract al dimension. Armed with this tool, we then show its practical use in predicting the performance of spatial access methods, and specifically of the Rtrees. We provide the jirst analysis of Rtrees for skewed distributions of points: We develop a formula that estimates the number of disk accesses for range queries, given only the fractal dimension of the point set, and its count. Experiments on real data sets show that the formula is very accurate: the relative error is usually below 5%, and it rarely exceeds 10%. We believe that the fractal dimension will help replace the uniformity and independence assumptions, allowing more accurate analysis for any spatial access method, as well as better estimates for query optimization on multiattribute queries. 1
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 147 (19 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...