Efficient Algorithms for the Weighted k-Center Problem on a Real Line

  • Danny Z. Chen
  • Haitao Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)


We present \(O(\min\{n\log^{1.5} n, n\log n+k^2\log^2\frac{n}{k}\log^2 n\})\) time algorithms for the weighted k-problem on a real line. Previously, the best known algorithms for this problem take O(nlog2 n) time, or O(knlogn) time, or a time linear in n but exponential in k. Our techniques involve developing efficient data structures for processing queries that find a lowest point in the common intersection of a certain subset of half-planes. This subproblem is interesting in its own right.


Internal Node Lower Point Interval Tree Demand Point Time Bound 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Danny Z. Chen
    • 1
  • Haitao Wang
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA

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