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377
An algorithm for finding best matches in logarithmic expected time
 ACM Transactions on Mathematical Software
, 1977
"... An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number of recor ..."
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Cited by 759 (2 self)
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An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number of records examined in each search is independent of the file size. The expected computation to perform each search is proportionalto 1ogN. Empirical evidence suggests that except for very small files, this algorithm is considerably faster than other methods.
Query evaluation techniques for large databases
 ACM COMPUTING SURVEYS
, 1993
"... Database management systems will continue to manage large data volumes. Thus, efficient algorithms for accessing and manipulating large sets and sequences will be required to provide acceptable performance. The advent of objectoriented and extensible database systems will not solve this problem. On ..."
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Cited by 758 (11 self)
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Database management systems will continue to manage large data volumes. Thus, efficient algorithms for accessing and manipulating large sets and sequences will be required to provide acceptable performance. The advent of objectoriented and extensible database systems will not solve this problem. On the contrary, modern data models exacerbate it: In order to manipulate large sets of complex objects as efficiently as today’s database systems manipulate simple records, query processing algorithms and software will become more complex, and a solid understanding of algorithm and architectural issues is essential for the designer of database management software. This survey provides a foundation for the design and implementation of query execution facilities in new database management systems. It describes a wide array of practical query evaluation techniques for both relational and postrelational database systems, including iterative execution of complex query evaluation plans, the duality of sort and hashbased set matching algorithms, types of parallel query execution and their implementation, and special operators for emerging database application domains.
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).
The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
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Cited by 535 (12 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
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 334 (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.
Approximating the nondominated front using the Pareto Archived Evolution Strategy
 EVOLUTIONARY COMPUTATION
, 2000
"... We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its ..."
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Cited by 324 (21 self)
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We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1 + 1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1 + 1)PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some realworld applications when local search seems superior to or competitive with populationbased methods. We introduce (1 + λ) and (μ  λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.
Geometric Range Searching and Its Relatives
 CONTEMPORARY MATHEMATICS
"... ... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems. ..."
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Cited by 273 (41 self)
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... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems.
Mesh Generation And Optimal Triangulation
, 1992
"... We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some cri ..."
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Cited by 213 (7 self)
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We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a fixed set of vertices and for the placement of new vertices (Steiner points). We briefly survey the heuristic algorithms used in some practical mesh generators.
Two Algorithms for NearestNeighbor Search in High Dimensions
, 1997
"... Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems aris ..."
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Cited by 201 (0 self)
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Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems arising in these applications can involve several hundred or several thousand dimensions. We consider the nearestneighbor problem for ddimensional Euclidean space: we wish to preprocess a database of n points so that given a query point, one can efficiently determine its nearest neighbors in the database. There is a large literature on algorithms for this problem, in both the exact and approximate cases. The more sophisticated algorithms typically achieve a query time that is logarithmic in n at the expense of an exponential dependence on the dimension d; indeed, even the averagecase analysis of heuristics such as kd trees reveals an exponential dependence on d in the query time. In this wor...
Multidimensional range queries in sensor networks
 in Proc. of the 1st international conference on Embedded networked sensor systems, SenSys
"... In many sensor networks, data or events are named by attributes. Many of these attributes have scalar values, so one natural way to query events of interest is to use a multidimensional range query. An example is: “List all events whose temperature lies between 50 ◦ and 60 ◦ , and whose light levels ..."
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Cited by 150 (13 self)
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In many sensor networks, data or events are named by attributes. Many of these attributes have scalar values, so one natural way to query events of interest is to use a multidimensional range query. An example is: “List all events whose temperature lies between 50 ◦ and 60 ◦ , and whose light levels lie between 10 and 15. ” Such queries are useful for correlating events occurring within the network. In this paper, we describe the design of a distributed index that scalably supports multidimensional range queries. Our distributed index for multidimensional data (or DIM) uses a novel geographic embedding of a classical index data structure, and is built upon the GPSR geographic routing algorithm. Our analysis reveals that, under reasonable assumptions about query distributions, DIMs scale quite well with network size (both insertion and query costs scale as O ( √ N)). In detailed simulations, we show that in practice, the insertion and query costs of other alternatives are sometimes an order of magnitude more than the costs of DIMs, even for moderately sized network. Finally, experiments on a small scale testbed validate the feasibility of DIMs.