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)

Abstract

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.

Keywords

Internal Node Lower Point Interval Tree Demand Point Time Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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