Summary: Approximation schemes for Euclidean kmedians and related
Sanjeev Arora #
Prabhakar Raghavan +
Satish Rao #
In the kmedian 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 solu
tion of cost at most 1 + 1/c times the optimum
and runs in time O(n O(c+1) ). The approxima
tion scheme also generalizes to some problems
related to kmedian.