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Nearoptimal hashing algorithms for approximate nearest neighbor in high dimensions
, 2008
"... In this article, we give an overview of efficient algorithms for the approximate and exact nearest neighbor problem. The goal is to preprocess a dataset of objects (e.g., images) so that later, given a new query object, one can quickly return the dataset object that is most similar to the query. The ..."
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Cited by 457 (7 self)
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In this article, we give an overview of efficient algorithms for the approximate and exact nearest neighbor problem. The goal is to preprocess a dataset of objects (e.g., images) so that later, given a new query object, one can quickly return the dataset object that is most similar to the query. The problem is of significant interest in a wide variety of areas.
Algorithms for dynamic geometric problems over data streams
 In STOC ’04: Proceedings of the thirtysixth annual ACM symposium on Theory of computing
, 2004
"... ..."
Coresets in Dynamic Geometric Data Streams
, 2005
"... A dynamic geometric data stream consists of a sequence of m insert/delete operations of points from the discrete space {1,..., ∆} d [26]. We develop streaming (1 + ɛ)approximation algorithms for kmedian, kmeans, MaxCut, maximum weighted matching (MaxWM), maximum travelling salesperson (MaxTSP), m ..."
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Cited by 34 (4 self)
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A dynamic geometric data stream consists of a sequence of m insert/delete operations of points from the discrete space {1,..., ∆} d [26]. We develop streaming (1 + ɛ)approximation algorithms for kmedian, kmeans, MaxCut, maximum weighted matching (MaxWM), maximum travelling salesperson (MaxTSP), maximum spanning tree (MaxST), and average distance over dynamic geometric data streams. Our algorithms maintain a small weighted set of points (a coreset) that approximates with probability 2/3 the current point set with respect to the considered problem during the m insert/delete operations of the data stream. They use poly(ɛ −1, log m, log ∆) space and update time per insert/delete operation for constant k and dimension d. Having a coreset one only needs a fast approximation algorithm for the weighted problem to compute a solution quickly. In fact, even an exponential algorithm is sometimes feasible as its running time may still be polynomial in n. For example one can compute in poly(log n, exp(O((1+log(1/ɛ)/ɛ) d−1))) time a solution to kmedian and kmeans [21] where n is the size of the current point set and k and d are constants. Finding an implicit solution to MaxCut can be done in poly(log n, exp((1/ɛ) O(1))) time. For MaxST and average distance we require poly(log n, ɛ −1) time and for MaxWM we require O(n 3) time to do this.
Sublineartime algorithms
 In Oded Goldreich, editor, Property Testing, volume 6390 of Lecture Notes in Computer Science
, 2010
"... In this paper we survey recent (up to end of 2009) advances in the area of sublineartime algorithms. 1 ..."
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Cited by 20 (2 self)
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In this paper we survey recent (up to end of 2009) advances in the area of sublineartime algorithms. 1
A SpaceOptimal DataStream Algorithm for Coresets in the Plane
"... Given a point set P ⊆ R², a subset Q ⊆ P is an εkernel of P if for every slab W containing Q, the (1+ε)expansion of W also contains P. We present a datastream algorithm for maintaining an εkernel of a stream of points in R² that uses O(1/√ε) space and takes O(log(1/ε)) amortized time to process ..."
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Cited by 19 (5 self)
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Given a point set P ⊆ R², a subset Q ⊆ P is an εkernel of P if for every slab W containing Q, the (1+ε)expansion of W also contains P. We present a datastream algorithm for maintaining an εkernel of a stream of points in R² that uses O(1/√ε) space and takes O(log(1/ε)) amortized time to process each point. This is the first spaceoptimal datastream algorithm for this problem. As a consequence, we obtain improved datastream approximation algorithms for other extent measures, such as width, robust kernels, as well as εkernels in higher dimensions.
KMedian Clustering, ModelBased Compressive Sensing, and Sparse Recovery for Earth Mover Distance
, 2011
"... We initiate the study of sparse recovery problems under the EarthMover Distance (EMD). Specifically, we design a distribution over m × n matrices A such that for any x, given Ax, we can recover a ksparse approximation to x under the EMD distance. One construction yields m = O(k log(n/k)) and a 1 + ..."
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Cited by 11 (4 self)
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We initiate the study of sparse recovery problems under the EarthMover Distance (EMD). Specifically, we design a distribution over m × n matrices A such that for any x, given Ax, we can recover a ksparse approximation to x under the EMD distance. One construction yields m = O(k log(n/k)) and a 1 + ɛ approximation factor, which matches the best achievable bound for other error measures, such as the ℓ1 norm. Our algorithms are obtained by exploiting novel connections to other problems and areas, such as streaming algorithms for kmedian clustering and modelbased compressive sensing. We also provide novel algorithms and results for the latter problems.
New LSHbased algorithm for approximate nearest neighbor
, 2005
"... We present an algorithm for capproximate nearest neighbor problem in a ddimensional Euclidean space, achieving query time of O(dn1/c 2+o(1)) and space O(dn+n1+1/c 2+o(1)). ..."
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Cited by 1 (0 self)
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We present an algorithm for capproximate nearest neighbor problem in a ddimensional Euclidean space, achieving query time of O(dn1/c 2+o(1)) and space O(dn+n1+1/c 2+o(1)).
A SpaceOptimal DataStream Algorithm for Coresets in the Plane ∗
"... Given a point set P ⊆ R 2, a subset Q ⊆ P is an εkernel of P if for every slab W containing Q, the (1 + ε)expansion of W also contains P. We present a datastream algorithm for maintaining an εkernel of a stream of points in R 2 that uses O(1 / √ ε) space and takes O(log(1/ε)) amortized time to ..."
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Given a point set P ⊆ R 2, a subset Q ⊆ P is an εkernel of P if for every slab W containing Q, the (1 + ε)expansion of W also contains P. We present a datastream algorithm for maintaining an εkernel of a stream of points in R 2 that uses O(1 / √ ε) space and takes O(log(1/ε)) amortized time to process each point. This is the first spaceoptimal datastream algorithm for this problem. 1