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Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality
, 1998
"... The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the ddimens ..."
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Cited by 715 (33 self)
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The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the ddimensional Euclidean space where X = ! d under some l p norm. Despite decades of effort, the current solutions are far from satisfactory; in fact, for large d, in theory or in practice, they provide little improvement over the bruteforce algorithm which compares the query point to each data point. Of late, there has been some interest in the approximate nearest neighbors problem, which is: Find a point p 2 P that is an fflapproximate nearest neighbor of the query q in that for all p 0 2 P , d(p; q) (1 + ffl)d(p 0 ; q). We present two algorithmic results for the approximate version that significantly improve the known bounds: (a) preprocessing cost polynomial in n and d, and a trul...
Similarity search in high dimensions via hashing
, 1999
"... The nearest or nearneighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search/index structures for performing similarity search over highdimensional data, e.g., image dat ..."
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Cited by 415 (12 self)
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The nearest or nearneighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search/index structures for performing similarity search over highdimensional data, e.g., image databases, document collections, timeseries databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the \curse of dimensionality. " That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in kd trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than bruteforce linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points
Nearest Neighbors In HighDimensional Spaces
, 2004
"... In this chapter we consider the following problem: given a set P of points in a highdimensional space, construct a data structure which given any query point q nds the point in P closest to q. This problem, called nearest neighbor search is of significant importance to several areas of computer sci ..."
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Cited by 76 (2 self)
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In this chapter we consider the following problem: given a set P of points in a highdimensional space, construct a data structure which given any query point q nds the point in P closest to q. This problem, called nearest neighbor search is of significant importance to several areas of computer science, including pattern recognition, searching in multimedial data, vector compression [GG91], computational statistics [DW82], and data mining. Many of these applications involve data sets which are very large (e.g., a database containing Web documents could contain over one billion documents). Moreover, the dimensionality of the points is usually large as well (e.g., in the order of a few hundred). Therefore, it is crucial to design algorithms which scale well with the database size as well as with the dimension. The nearestneighbor problem is an example of a large class of proximity problems, which, roughly speaking, are problems whose definitions involve the notion of...
Low Latency Photon Mapping Using Block Hashing
 IN PROCEEDINGS OF THE CONFERENCE ON GRAPHICS HARDWARE 2002
, 2002
"... Photon mapping is useful in the acceleration of global illumination and caustic effects computed by path tracing. For hardware accelerated rendering, photon maps would be especially useful for simulating caustic lighting effects on nonLambertian surfaces. For this to be possible, an efficient hardw ..."
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Cited by 21 (1 self)
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Photon mapping is useful in the acceleration of global illumination and caustic effects computed by path tracing. For hardware accelerated rendering, photon maps would be especially useful for simulating caustic lighting effects on nonLambertian surfaces. For this to be possible, an efficient hardware algorithm for the computation of the k nearest neighbours to a sample point is required. Existing
NNH: Improving Performance of NearestNeighbor Searches Using Histograms
 IN EDBT
, 2003
"... Efficient search for nearest neighbors (NN) is a fundamental problem arising in a large variety of applications of vast practical interest. In this paper we propose a novel technique, called NNH ("Nearest Neighbor Histograms"), which uses specific histogram structures to improve the performance ..."
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Cited by 6 (3 self)
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Efficient search for nearest neighbors (NN) is a fundamental problem arising in a large variety of applications of vast practical interest. In this paper we propose a novel technique, called NNH ("Nearest Neighbor Histograms"), which uses specific histogram structures to improve the performance of NN search algorithms. A primary feature of our proposal is that such histogram structures can coexist in conjunction with a plethora of NN search algorithms without the need to substantially modify them. The main idea behind our proposal is to choose a small number of pivot objects in the space, and precalculate the distances to their nearest neighbors. We provide a complete specification of such histogram structures and show how to make use of the information they provide towards more e#ective searching. In particular, we show how to construct them, how to decide the number of pivots, how to choose pivot objects, how to incrementally maintain them under dynamic updates, and how to utilize them in conjunction with a variety of NN search algorithms to improve the performance of NN searches. Our intensive experiments show that nearest neighbor histograms can be efficiently constructed and maintained, and when used in conjunction with a variety of algorithms for NN search, they can improve the performance dramatically.
On Some Communication Schemes for Distributed PursuitEvasion Games
"... A probabilistic pursuitevasion game from the literature is used as an example to study constrained communication in multirobot systems. Communication protocols based on timetriggered and eventtriggered synchronization schemes are considered. It is shown that by limiting the communication to eve ..."
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Cited by 2 (1 self)
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A probabilistic pursuitevasion game from the literature is used as an example to study constrained communication in multirobot systems. Communication protocols based on timetriggered and eventtriggered synchronization schemes are considered. It is shown that by limiting the communication to events when the probabilistic map updated by the individual pursuer contains new information, as measured through a map entropy, the utilization of the communication link can be considerably improved compared to conventional timetriggered communication.
Nearest Neighbor Monitoring of Spatial Queries in Wireless Environments
"... In a Wireless data broadcast is a promising technique for information dissemination that leverages the computational capabilities of the mobile devices in order to enhance the scalability of the system. Under this environment, the data are continuously broadcast by the server, interleaved with some ..."
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In a Wireless data broadcast is a promising technique for information dissemination that leverages the computational capabilities of the mobile devices in order to enhance the scalability of the system. Under this environment, the data are continuously broadcast by the server, interleaved with some indexing information for query processing. Clients may then tune in the broadcast channel and process their queries locally without contacting the server. We propose a novel technique, called NNH (“Nearest Neighbor Histograms”), which uses specific histogram structures to improve the performance of NN search algorithms. A primary feature of our proposal is that such histogram structures can coexist in conjunction with a plethora of NN search algorithms without the need to substantially modify them. The main idea behind our proposal is to choose a small number of pivot objects in the space, and precalculate the distances to their nearest neighbors.
Reporting Neighbors in HighDimensional Euclidean Space ∗
"... We consider the following problem, which arises in many database and webbased applications: Given a set P of n points in a highdimensional space Rd and a distance r, we want to report all pairs of points of P at Euclidean distance at most r. We present two randomized algorithms, one based on rando ..."
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We consider the following problem, which arises in many database and webbased applications: Given a set P of n points in a highdimensional space Rd and a distance r, we want to report all pairs of points of P at Euclidean distance at most r. We present two randomized algorithms, one based on randomly shifted grids, and the other on randomly shifted and rotated grids. The running time of both algorithms is of the form C(d)(n + k) log n, where k is the output size and C(d) is a constant that depends on the dimension d. The log n factor is needed to guarantee, with high probability, that all neighbor pairs are reported, and can be dropped if it suffices to report, in expectation, an arbitrarily large fraction of the pairs. When only translations are used, C(d) is of the form (a √ d) d, for some (small) absolute constant a ≈ 0.484; this bound is worstcase tight, up to an exponential factor of about 2 d. When both rotations and translations are used, C(d) can be improved to roughly 6.74 d, getting rid of the superexponential factor √ d d. When the input set (lies in a subset of dspace that) has low doubling dimension δ, the performance of the first algorithm improves to C(d, δ)(n + k) log n (or to C(d, δ)(n + k)), where C(d, δ) = O((ed/δ) δ), for δ ≤ √ ( d. Otherwise, C(d, δ) = O e √ d √ d δ) We also present experimental results on several large datasets, demonstrating that our algorithms run significantly faster than all the leading existing algorithms for reporting neighbors. ∗Work by Haim Kaplan and Micha Sharir has been supported