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The grid file: an adaptable, symmetric multikey file structure
 In Trends in Information Processing Systems, Proc. 3rd ECZ Conference, A. Duijvestijn and P. Lockemann, Eds., Lecture Notes in Computer Science 123
, 1981
"... Traditional file structures that provide multikey access to records, for example, inverted files, are extensions of file structures originally designed for singlekey access. They manifest various deficiencies in particular for multikey access to highly dynamic files. We study the dynamic aspects of ..."
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Cited by 386 (4 self)
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Traditional file structures that provide multikey access to records, for example, inverted files, are extensions of file structures originally designed for singlekey access. They manifest various deficiencies in particular for multikey access to highly dynamic files. We study the dynamic aspects of tile structures that treat all keys symmetrically, that is, file structures which avoid the distinction between primary and secondary keys. We start from a bitmap approach and treat the problem of file design as one of data compression of a large sparse matrix. This leads to the notions of a grid partition of the search space and of a grid directory, which are the keys to a dynamic file structure called the grid file. This tile system adapts gracefully to its contents under insertions and deletions, and thus achieves an upper hound of two disk accesses for single record retrieval; it also handles range queries and partially specified queries efficiently. We discuss in detail the design decisions that led to the grid file, present simulation results of its behavior, and compare it to other multikey access file structures.
Efficient MultiObject Dynamic Query Histograms
 Proc. of Information Visualization
, 1999
"... Dynamic Queries offer continuous feedback during range queries, and have been shown to be effective and satisfying. Recent work has extended them to datasets of 100,000 objects and, separately, to queries involving relations among multiple objects. The latter work enables filtering houses by propert ..."
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Cited by 11 (1 self)
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Dynamic Queries offer continuous feedback during range queries, and have been shown to be effective and satisfying. Recent work has extended them to datasets of 100,000 objects and, separately, to queries involving relations among multiple objects. The latter work enables filtering houses by properties of their owners, for instance. Our primary concern is providing feedback from histograms during Dynamic Query. The height of each histogram bar shows the count of selected objects whose attribute value falls into a given range. Unfortunately, previous efficient algorithms for single object queries overcount in the case of multiple objects if, for instance, a house has multiple owners. This paper presents an efficient algorithm that with high probability closely approximates the true counts. 1. Previous Dynamic Query work 1.1. Single Object Interface Figure 1 shows a Dynamic Query (DQ) interface as implemented in VQE, a Visual Query Environment for exploring data from a database [1]. ...
Finding kClosestPairs Efficiently for High Dimensional Data
, 2000
"... We present a novel approach to report approximate as well as exact kclosest pairs for sets of high dimensional points, under the L t metric, t = 1; : : : ; 1. The proposed algorithms are efficient and simple to implement. They all use multiple shifted copies of the data points sorted according to ..."
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Cited by 6 (0 self)
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We present a novel approach to report approximate as well as exact kclosest pairs for sets of high dimensional points, under the L t metric, t = 1; : : : ; 1. The proposed algorithms are efficient and simple to implement. They all use multiple shifted copies of the data points sorted according to their position along a space filling curve, such as the Peano curve, in a way that allows us to make performance guarantees and without assuming that the dimensionality d is constant. The first algorithm computes an O(d 1+1=t ) approximation to the k th closest pair distance in O(d 2 n log +dk(d + log k)) time. Experimental results, obtained using various real data sets of varying dimensions, indicate that the approximation factor is much better in practice. In the second algorithm we use this approximation in order to find the exact k closest pairs in O(dM) additional time, where M is the number of points in certain short subsegments of the spacefilling curve. The exact algorithm is ...
kd range search with binary patricia tries
, 2004
"... We use Patricia tries to represent textual and spatial data, and present a range search algorithm for reporting all kd records from a set of size n intersecting a query rectangle. Data and queries include both textual and spatial data. Patricia tries are evaluated experimentally (for n up to 1,000, ..."
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Cited by 3 (1 self)
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We use Patricia tries to represent textual and spatial data, and present a range search algorithm for reporting all kd records from a set of size n intersecting a query rectangle. Data and queries include both textual and spatial data. Patricia tries are evaluated experimentally (for n up to 1,000,000) using uniform distributed random spatial data and textual data selected from the Canadian toponymy. We compared the performance of the Patricia trie for kd points, kd rectangles and kd combined textual and spatial data to the kd tree, R ∗tree, Ternary Search Trie and the naive method. Overall, our experiments show that Patricia tries are the best when F ∈ [0, log 2 n] (F is the number of data in range). The expected range search time for Patricia tries was determined theoretically, and found to agree with experimental results when 2 ≤ k ≤ 20.
Approximate Range Searching In The Absolute Error Model
, 2007
"... Range searching is a well known problem in computational geometry. We consider this problem in the context of approximation, where an approximation parameter ε > 0 is provided. Most prior work on this problem has focused on the relative error model, where each range shape R is bounded, and points ..."
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Cited by 2 (2 self)
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Range searching is a well known problem in computational geometry. We consider this problem in the context of approximation, where an approximation parameter ε > 0 is provided. Most prior work on this problem has focused on the relative error model, where each range shape R is bounded, and points within distance ε · diam(R) of the range’s boundary may or may not be included. We introduce a different approximation model, called the absolute error model, in which points within distance ε of the range’s boundary may or may not be included, regardless of the diameter of the range. We consider sets of ranges consisting of general convex bodies, axisaligned rectangles, halfspaces, Euclidean balls, and simplices. We examine a variety of problem formulations, including range searching under general commutative semigroups, idempotent semigroups, groups, range emptiness, and range reporting. We apply our data structures to several related problems, including range sketching, approximate nearest neighbor searching, exact idempotent range searching, approximate range searching in the data stream model, and
Geometric Retrieval for Grid Points in the RAM Model
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
"... We consider the problem of ddimensional searching (d 3) for four query types: range, partial range, exact match and partial match searching. Let N be the number of points, s be the number of keys specified in a partial match and partial range query and t be the number of points retrieved. We pre ..."
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Cited by 1 (1 self)
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We consider the problem of ddimensional searching (d 3) for four query types: range, partial range, exact match and partial match searching. Let N be the number of points, s be the number of keys specified in a partial match and partial range query and t be the number of points retrieved. We present a data structure with worst case time complexities O(t + log N), O(t + (d s) + log N), O(d + # log N) and O(t + (d s) + s # log N) for each of the aforementioned query types respectively. We also present a second, more concrete solution for exact and partial match queries, which achieves the same query time but has di#erent space requirements. The proposed data structures are considered in the RAM model of computation.
Smooth Data Modelling and . . .
"... On the basis of studies of the olfactory bulb of a rabbit Freeman suggested that in the rest state the dynamics of this neural cluster is chaotic, but that when a familiar scent is presented the neural system rapidly simplifies its behaviour and the dynamics becomes more orderly, more nearly periodi ..."
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On the basis of studies of the olfactory bulb of a rabbit Freeman suggested that in the rest state the dynamics of this neural cluster is chaotic, but that when a familiar scent is presented the neural system rapidly simplifies its behaviour and the dynamics becomes more orderly, more nearly periodic than when in the rest state. This suggests an interesting model of recognition in biological neural systems. To realise this in an artificial neural system, some form of control of the chaotic neural behaviour is necessary to achieve periodic dynamical behaviour when a stimulus is presented. In this thesis we first study the general problem of modelling smooth systems and introduce a number of useful techniques relevant to the problem of modelling chaotic dynamics. After a preliminary review of chaotic dynamical systems and their control, and discussing several examples of neural chaos, we then construct a chaotic neural model. We show how this model can be successfully controlled using several different parametric control methods. However, such methods of control are external to the network and we are interested in the control of higher dimensional networks using a technique which is intrinsic to the neural dynamics. Using a higher dimensional system we investigate several methods of control and conclude that
Approximate Orthogonal Range Search using
, 2005
"... We use Patricia tries to answer ɛapproximate orthogonal range search on a set of n random points and rectangles in kdimensional space. Given n kdimensional random points or rectangles and a kdimensional query rectangle, ɛapproximate orthogonal range query counts (or reports) the points in the q ..."
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We use Patricia tries to answer ɛapproximate orthogonal range search on a set of n random points and rectangles in kdimensional space. Given n kdimensional random points or rectangles and a kdimensional query rectangle, ɛapproximate orthogonal range query counts (or reports) the points in the query rectangle or the rectangles intersecting the query rectangle, allowing errors near the boundary of the query rectangle. Points within a distance of a function of ɛ the boundary of the query rectangle might be misclassified. The approximate orthogonal range search time using Patricia tries is determined theoretically to be O(k log n/ɛ k−1) for cubical range queries. Patricia tries are evaluated experimentally for ɛapproximate orthogonal range counting and reporting queries (for 2 ≤ k ≤ 10 and n up to 1,000,000) using uniformly distributed random points and rectangles, and we compared the
AN ANALYSIS OF RANDOM dDIMENSIONAL QUAD TREES* LUC DEVRDYEt AND LOUISE LAFDREST$
"... Abstract. It is shown that the depth of the last node inserted in a random quad tree constructed from independent uniform [Q, 11 d random vectors is in probability asymptotic to (2/d) log n, where log denotes the natural logarithm. In addition, for d =2, exact values are obtained for all the moments ..."
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Abstract. It is shown that the depth of the last node inserted in a random quad tree constructed from independent uniform [Q, 11 d random vectors is in probability asymptotic to (2/d) log n, where log denotes the natural logarithm. In addition, for d =2, exact values are obtained for all the moments of the depth of the last node. Key words. average time analysis, probability ineq ' alities, random quad tree, multidimensional data structures, search tree, expected behavior, analysis of a;orithms