
Approximation Algorithms For The Euclidean Dispersion Problems
In this article, we consider the Euclidean dispersion problems. Let P={p...
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Approximation Algorithms For The Dispersion Problems in a Metric Space
In this article, we consider the cdispersion problem in a metric space ...
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Dimensionality's Blessing: Clustering Images by Underlying Distribution
Many high dimensional vector distances tend to a constant. This is typic...
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A constant parameterized approximation for hardcapacitated kmeans
Hardcapacitated kmeans (HCKM) is one of the remaining fundamental prob...
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Faster Projective Clustering Approximation of Big Data
In projective clustering we are given a set of n points in R^d and wish ...
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Sparse PCA via Bipartite Matchings
We consider the following multicomponent sparse PCA problem: given a se...
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Robust kCenter with Two Types of Radii
In the nonuniform kcenter problem, the objective is to cover points in...
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MinSum Clustering (with Outliers)
We give a constant factor polynomial time pseudoapproximation algorithm for minsum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to compute a solution that clusters 98% of the input data points and pays no more than a constant factor times the optimal solution that clusters 99% of the input data points. More generally, we give the following bicriteria approximation: For any > 0, for any instance with n input points and for any positive integer n'≤ n, we compute in polynomial time a clustering of at least (1) n' points of cost at most a constant factor greater than the optimal cost of clustering n' points. The approximation guarantee grows with 1/. Our results apply to instances of points in real space endowed with squared Euclidean distance, as well as to points in a metric space, where the number of clusters, and also the dimension if relevant, is arbitrary (part of the input, not an absolute constant).
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