The Euclidean k-Supplier Problem

The k -supplier problem is a fundamental location problem that involves opening k facilities to minimize the maximum distance of any client to an open facility. We consider the k -supplier problem in Euclidean metrics (of arbitrary dimension) and present an algorithm with approximation ratio 1 + 3 < 2.74 . This improves upon the previously known 3-approximation algorithm, which also holds for general metrics. Our result is almost best possible as the Euclidean k -supplier problem is NP-hard to approximate better than a factor of 7 > 2.64 . We also present a nearly linear time algorithm for the Euclidean k -supplier in constant dimensions that achieves an approximation ratio better than three.