Philip S. Yu, Joel L. Wolf, et al.
IS&T/SPIE Electronic Imaging 1995
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.
Philip S. Yu, Joel L. Wolf, et al.
IS&T/SPIE Electronic Imaging 1995
Kanthi Sarpatwar, Baruch Schieber, et al.
FSTTCS 2019
Yishay Mansour, Baruch Schieber, et al.
Journal of the ACM
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SIAM Journal on Computing