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.
This research was supported in part by NSF under Grant CCF-0916606.
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Chen, D.Z., Wang, H. (2011). Efficient Algorithms for the Weighted k-Center Problem on a Real Line. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_60
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DOI: https://doi.org/10.1007/978-3-642-25591-5_60
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