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Proximity Algorithms for Nearly Doubling Spaces

2013
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SIAM Journal on Discrete Mathematics
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We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d * , remove from S the fewest number of points so that the remaining set has doubling dimension at most d * . We present a bicriteria approximation for this problem, and extend this algorithm to solve a group of proximity problems. d * (or equivalently, target doubling constant λ * = 2 d * ). We thus call a data set nearly-doubling if all but a negligible fraction of the points have bounded

doi:10.1137/120874242
fatcat:hzlzfl4iprc5phwa34ciinsohe