Computing k-center over streaming data for small k

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Computing k-center over streaming data for small k

The Euclidean k-center problem is to compute k congruent balls covering a given set of points in Rd such that the radius is minimized. We consider the k-center problem in R-d for k = 2,3 in a single-pass streaming model, where data is allowed to be examined once and only a small amount of information can be stored in a device. We present two approximation algorithms whose space complexity does not depend on the size of the input data. The first algorithm guarantees a (2+epsilon)-factor using O(d/epsilon) space in arbitrary dimensions, and the second algorithm guarantees a (1+epsilon)-factor using O(1/epsilon(d)) space in constant dimensions. The same algorithms can be used to compute a k-center under any L-p metric for k = 2, 3.111sciescopu