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Mtree: An Efficient Access Method for Similarity Search in Metric Spaces
, 1997
"... A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion o ..."
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Cited by 663 (38 self)
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A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion of objects and split management, whF h keep th Mtree always balanced  severalheralvFV split alternatives are considered and experimentally evaluated. Algorithd for similarity (range and knearest neigh bors) queries are also described. Results from extensive experimentationwith a prototype system are reported, considering as th performance criteria th number of page I/O's and th number of distance computations. Th results demonstratethm th Mtree indeed extendsth domain of applicability beyond th traditional vector spaces, performs reasonably well inhE[94Kv#E44V[vh data spaces, and scales well in case of growing files. 1
A quantitative analysis and performance study for similaritysearch methods in high dimensional spaces, in:
 Proceedings of the 24th VLDB International Conference on Very Large Data Bases,
, 1998
"... ..."
Nearest neighbor queries.
 ACM SIGMOD Record,
, 1995
"... Abstract A frequently encountered type of query in Geographic Information Systems is to nd the k nearest neighbor objects to a given point in space. Processing such queries requires substantially di erent search algorithms than those for location or range queries. In this paper we present a n e cie ..."
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Cited by 592 (1 self)
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Abstract A frequently encountered type of query in Geographic Information Systems is to nd the k nearest neighbor objects to a given point in space. Processing such queries requires substantially di erent search algorithms than those for location or range queries. In this paper we present a n e cient branchandbound Rtree traversal algorithm to nd the nearest neighbor object to a point, and then generalize it to nding the k nearest neighbors. We also discuss metrics for an optimistic and a pessimistic search ordering strategy as well as for pruning. Finally, w e 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.
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 237 (18 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 217 (16 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...
An Introduction to Spatial Database Systems
 THE VLDB JOURNAL
, 1994
"... We propose a definition of a spatial database system as a database system that offers spatial data types in its data model and query language, and supports ..."
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Cited by 214 (9 self)
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We propose a definition of a spatial database system as a database system that offers spatial data types in its data model and query language, and supports
Progressive Skyline Computation in Database Systems
 ACM TRANS. DATABASE SYST
, 2005
"... The skyline of a ddimensional dataset contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive methods that can quickly return the initial results without r ..."
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Cited by 205 (13 self)
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The skyline of a ddimensional dataset contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive methods that can quickly return the initial results without reading the entire database. All the existing algorithms, however, have some serious shortcomings which limit their applicability in practice. In this article we develop branch skyline (BBS), an algorithm based on nearestneighbor search, which is I/O optimal, that is, it performs a single access only to those nodes that may contain skyline points. BBS is simple to implement and supports all types of progressive processing (e.g., user preferences, arbitrary dimensionality, etc). Furthermore, we propose several interesting variations of skyline computation, and show how BBS can be applied for their efficient processing.
Continuous Nearest Neighbor Search
, 2002
"... A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., "find all my nearest gas stations during my route from point s to point e"). The result contains a set of <point, interval> tuples, such that point is the NN of all po ..."
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Cited by 160 (10 self)
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A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., "find all my nearest gas stations during my route from point s to point e"). The result contains a set of <point, interval> tuples, such that point is the NN of all points in the corresponding interval. Existing methods for continuous nearest neighbor search are based on the repetitive application of simple NN algorithms, which incurs significant overhead. In this paper we propose techniques that solve the problem by performing a single query for the whole input segment. As a result the cost, depending on the query and dataset characteristics, may drop by orders of magnitude.
A Simple Algorithm for Nearest Neighbor Search in High Dimensions
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Abstract—The problem of finding the closest point in highdimensional spaces is common in pattern recognition. Unfortunately, the complexity of most existing search algorithms, such as kd tree and Rtree, grows exponentially with dimension, making them impractical for dimensionality above 15. In ne ..."
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Cited by 153 (1 self)
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Abstract—The problem of finding the closest point in highdimensional spaces is common in pattern recognition. Unfortunately, the complexity of most existing search algorithms, such as kd tree and Rtree, grows exponentially with dimension, making them impractical for dimensionality above 15. In nearly all applications, the closest point is of interest only if it lies within a userspecified distance e. We present a simple and practical algorithm to efficiently search for the nearest neighbor within Euclidean distance e. The use of projection search combined with a novel data structure dramatically improves performance in high dimensions. A complexity analysis is presented which helps to automatically determine e in structured problems. A comprehensive set of benchmarks clearly shows the superiority of the proposed algorithm for a variety of structured and unstructured search problems. Object recognition is demonstrated as an example application. The simplicity of the algorithm makes it possible to construct an inexpensive hardware search engine which can be 100 times faster than its software equivalent. A C++ implementation of our algorithm is available upon request to search@cs.columbia.edu/CAVE/.
Query Processing in Spatial Network Databases
 In VLDB
, 2003
"... Despite the importance of spatial networks in reallife applications, most of the spatial database literature focuses on Euclidean spaces. In this paper we propose an architecture that integrates network and Euclidean information, capturing pragmatic constraints. Based on this architecture, we ..."
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Cited by 140 (7 self)
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Despite the importance of spatial networks in reallife applications, most of the spatial database literature focuses on Euclidean spaces. In this paper we propose an architecture that integrates network and Euclidean information, capturing pragmatic constraints. Based on this architecture, we develop a Euclidean restriction and a network expansion framework that take advantage of location and connectivity to efficiently prune the search space. These frameworks are successfully applied to the most popular spatial queries, namely nearest neighbors, range search, closest pairs and edistance joins, in the context of spatial network databases.