The Weighted k-Center Problem in Trees for Fixed k

Authors Binay Bhattacharya, Sandip Das, Subhadeep Ranjan Dev

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Author Details

Binay Bhattacharya
  • Simon Fraser University, Burnaby, Canada
Sandip Das
  • Indian Statistical Institute, Kolkata, India
Subhadeep Ranjan Dev
  • Indian Statistical Institute, Kolkata, India

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Binay Bhattacharya, Sandip Das, and Subhadeep Ranjan Dev. The Weighted k-Center Problem in Trees for Fixed k. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 27:1-27:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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. [Haitao Wang and Jingru Zhang, 2018]. Whether an O(n) time algorithm exists for arbitrary k is still open.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Network optimization
  • facility location
  • prune and search
  • parametric search
  • k-center problem
  • conditional k-center problem
  • trees


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