A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
SIAM Journal on Computing
An algorithm for approximate closest-point queries
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Nearly linear time approximation schemes for Euclidean TSP and other geometric problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A Nearly Linear-Time Approximation Scheme for the Euclidean $k$-Median Problem
SIAM Journal on Computing
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
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In the k-supplier problem, we are given a set of clients C and set of facilities F located in a metric (C∪F, d), along with a bound k. The goal is to open a subset of k facilities so as to minimize the maximum distance of a client to an open facility, i.e., min S⊆F: |S|=k max v∈Cd(v,S), where d(v,S)= min u∈Sd(v,u) is the minimum distance of client v to any facility in S. We present a $1+\sqrt{3}k-supplier problem in Euclidean metrics. This improves the previously known 3-approximation algorithm [9] which also holds for general metrics (where it is known to be tight). It is NP-hard to approximate Euclidean k-supplier to better than a factor of $\sqrt{7}\approx 2.65$, even in dimension two [5]. Our algorithm is based on a relation to the edge cover problem. We also present a nearly linear O(n·log2n) time algorithm for Euclidean k-supplier in constant dimensions that achieves an approximation ratio of 2.965, where n=|C∪F|.