Efficient algorithms for the weighted k-center problem on a real line

Authors:
Danny Z. Chen;Haitao Wang
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

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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(nlog2n) 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.