Approximation schemes for Euclidean k-Medians And Related Problems (1998) [89 citations — 4 self]
http://www.cs.princeton.edu/~arora/pubs/facility.p
http://www.almaden.ibm.com/cs/k53/./algopapers/sto
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author = {Sanjeev Arora and Prabhakar Raghavan and Satish Rao},
title = {Approximation schemes for Euclidean k-Medians And Related Problems},
booktitle = {In Proc. 30th Annu. ACM Sympos. Theory Comput},
year = {1998},
pages = {106--113}
}
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Abstract:
In the k-median problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances from each of the points of S to the nearest median is minimized. This paper gives an approximation scheme for the plane that for any c > 0 produces a solution of cost at most 1 + 1/c times the optimum and runs in time O(n O(c+1) ). The approximation scheme also generalizes to some problems related to k-median. Our methodology is to extend Arora's [1, 2] techniques for the TSP, which hitherto seemed inapplicable to problems such as the k-median problem. 1 Introduction In the k-median problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in the space, such that the sum of the distances from each of the points of S to the nearest median is minimized. Besides its intrinsic appeal as a cleanly-stated, basic unsolved problem in combinatorial optimizatio...
