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Abstract:
We give an improved approximation algorithm for the general kmedians problem. Given any \epsilon>0, the algorithm finds a solution of total distance at most D(1+\epsilon) using at most k ln(n+n/\epsilon) medians (a.k.a. sites), provided some solution of total distance D using k medians exists. This improves over the best previous bound (w.r.t. the number of medians) by a factor of \Omega(1/\epsilon) provided 1/\epsilon=n^O(1). The algorithm is a greedy algorithm, derived using the method of oblivious randomized rounding. It requires at most k ln(n+n/\epsilon) lineartime iterations. We also derive algorithms for fractional and weighted variants of the problem.
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Neal E. Young,
"Greedy Approximation Algorithms for KMedians by Randomized Rounding."
Dartmouth Computer Science Technical Report PCSTR99344,
March 1999.
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