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A constantfactor approximation algorithm for the kmedian problem
 In Proceedings of the 31st Annual ACM Symposium on Theory of Computing
, 1999
"... We present the first constantfactor approximation algorithm for the metric kmedian problem. The kmedian problem is one of the most wellstudied clustering problems, i.e., those problems in which the aim is to partition a given set of points into clusters so that the points within a cluster are re ..."
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Cited by 249 (13 self)
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are relatively close with respect to some measure. For the metric kmedian problem, we are given n points in a metric space. We select k of these to be cluster centers, and then assign each point to its closest selected center. If point j is assigned to a center i, the cost incurred is proportional
Medians and Beyond: New Aggregation Techniques for Sensor Networks
, 2004
"... Wireless sensor networks offer the potential to span and monitor large geographical areas inexpensively. Sensors, however, have significant power constraint (battery life), making communication very expensive. Another important issue in the context of sensorbased information systems is that individu ..."
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Cited by 190 (6 self)
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is that individual sensor readings are inherently unreliable. In order to address these two aspects, sensor database systems like TinyDB and Cougar enable innetwork data aggregation to reduce the communication cost and improve reliability. The existing data aggregation techniques, however, are limited to relatively
Approximation schemes for Euclidean kMedians And Related Problems
 In Proc. 30th Annu. ACM Sympos. Theory Comput
, 1998
"... In the kmedian problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances from each of the points of S to the nearest median is minimized. This paper gives an approximation scheme for the plane that ..."
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Cited by 142 (3 self)
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that for any c > 0 produces a solution of cost at most 1 + 1/c times the optimum and runs in time O(n O(c+1) ). The approximation scheme also generalizes to some problems related to kmedian. Our methodology is to extend Arora's [1, 2] techniques for the TSP, which hitherto seemed inapplicable
The Complexity of Computing Medians of Relations
, 1998
"... Let N be a finite set and R be the set of all binary relations on N . Consider R endowed with a metric d, the symmetric difference distance. For a given mtuple = (R 1 ; : : : ; Rm ) 2 R m , a relation R 2 R that minimizes the function P m k=1 d(R k ; R) is called a median relation of . In the socia ..."
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Cited by 22 (0 self)
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Let N be a finite set and R be the set of all binary relations on N . Consider R endowed with a metric d, the symmetric difference distance. For a given mtuple = (R 1 ; : : : ; Rm ) 2 R m , a relation R 2 R that minimizes the function P m k=1 d(R k ; R) is called a median relation
Parameter Estimation Techniques: A Tutorial with Application to Conic Fitting
, 1995
"... Almost all problems in computer vision are related in one form or another to the problem of estimating parameters from noisy data. In this tutorial, we present what is probably the most commonly used techniques for parameter estimation. These include linear leastsquares (pseudoinverse and eigen a ..."
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Cited by 278 (8 self)
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Almost all problems in computer vision are related in one form or another to the problem of estimating parameters from noisy data. In this tutorial, we present what is probably the most commonly used techniques for parameter estimation. These include linear leastsquares (pseudoinverse and eigen
Wavelet Thresholding via a Bayesian Approach
 J. R. STATIST. SOC. B
, 1996
"... We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed to capture the sparseness of wavelet expansion common to most applications. ..."
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Cited by 262 (33 self)
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. For the prior specified, the posterior median yields a thresholding procedure. Our prior model for the underlying function can be adjusted to give functions falling in any specific Besov space. We establish a relation between the hyperparameters of the prior model and the parameters of those Besov spaces within
The Online Median Problem
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... We introduce a natural variant of the (metric uncapacitated) kmedian problem that we call the online median problem. Whereas the kmedian problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities ar ..."
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Cited by 82 (2 self)
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to that of an optimal offline placement. Our main result is a lineartime constantcompetitive algorithm for the online median problem. In addition, we present a related, though substantially simpler, lineartime constantfactor approximation algorithm for the (metric uncapacitated) facility location problem
A Comparison of Prediction Accuracy, Complexity, and Training Time of Thirtythree Old and New Classification Algorithms
, 2000
"... . Twentytwo decision tree, nine statistical, and two neural network algorithms are compared on thirtytwo datasets in terms of classication accuracy, training time, and (in the case of trees) number of leaves. Classication accuracy is measured by mean error rate and mean rank of error rate. Both cr ..."
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Cited by 234 (8 self)
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algorithm is Quest with linear splits, which ranks fourth and fth, respectively. Although splinebased statistical algorithms tend to have good accuracy, they also require relatively long training times. Polyclass, for example, is third last in terms of median training time. It often requires hours
The quantum query complexity of approximating the median and related statistics
 STOC'99
, 1999
"... Let X = (z,, , z,,) be a sequence of n numbers. For 6> 0, we say that 5; is an eapproximate median if the number of elements strictly less than zi and the number of elements strictly greater than zi are each less than (1 + 6):. We consider the quantum query complexity of computing an capprox ..."
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Cited by 74 (1 self)
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Let X = (z,, , z,,) be a sequence of n numbers. For 6> 0, we say that 5; is an eapproximate median if the number of elements strictly less than zi and the number of elements strictly greater than zi are each less than (1 + 6):. We consider the quantum query complexity of computing an c
On median graphs and median grid graphs
"... Let G be a Q4free median graph on n vertices and m edges. Let k be the number of equivalence classes of DjokovićWinkler’s relation Θ and let h be the number of Q3’s in G. Then we prove that 2n −m − k + h = 2. We also characterize median grid graphs in several different ways, for instance, they ar ..."
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Let G be a Q4free median graph on n vertices and m edges. Let k be the number of equivalence classes of DjokovićWinkler’s relation Θ and let h be the number of Q3’s in G. Then we prove that 2n −m − k + h = 2. We also characterize median grid graphs in several different ways, for instance
Results 1  10
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7,237