Abstract
Given a set P of n elements, and a function d that assigns a non-negative real number d(p, q) for each pair of elements \(p,q \in P\), we want to find a subset \(S\subseteq P\) with \(|S|=k\) such that \(\mathop {\mathrm {cost}}(S)= \min \{ d(p,q) \mid p,q \in S\}\) is maximized. This is the max-min k-dispersion problem. In this paper, exact algorithms for the max-min k-dispersion problem are studied. We first show the max-min k-dispersion problem can be solved in \(O(n^{\omega k/3} \log n)\) time. Then, we show two special cases in which we can solve the problem quickly. Namely, we study the cases where a set of n points lie on a line and where a set of n points lie on a circle (and the distance is measured by the shortest arc length on the circle). We obtain O(n)-time algorithms after sorting.
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Akagi, T. et al. (2018). Exact Algorithms for the Max-Min Dispersion Problem. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_20
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DOI: https://doi.org/10.1007/978-3-319-78455-7_20
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