Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
SIAM Journal on Computing
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Discrete & Computational Geometry
Approximating extent measures of points
Journal of the ACM (JACM)
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Proceedings of the twenty-fourth annual symposium on Computational geometry
A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Let P be a set of n points in d-dimensional Euclidean space, where each of the points has integer coordinates from the range [−Δ, Δ], for some Δ ≥ 2. Let ε 0 be a given parameter. We show that there is subset Q of P, whose size is polynomial in (log Δ)/ε, such that for any k slabs that cover Q, their ε-expansion covers P. In this result, k and d are assumed to be constants. The set Q can also be computed efficiently, in time that is roughly n times the bound on the size of Q. Besides yielding approximation algorithms that are linear in n and polynomial in log Δ for the k-slab cover problem, this result also yields small coresets and efficient algorithms for several other clustering problems.