The Weighted k-Center Problem in Trees for Fixed k.

We present a linear time algorithm for the weighted k-center problem on trees for fixed k. This partially settles the long-standing question about the lower bound on the time complexity of the problem. The current time complexity of the best-known algorithm for the problem with k as part of the input is O(n log n) by Wang et al. (2018) [20]. Whether an O(n) time algorithm exists for arbitrary k is still open. (c) 2022 Elsevier B.V. All rights reserved.