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arXiv · 1804.00241

Assigning Weights to Minimize the Covering Radius in the Plane

Eunjin Oh·Hee-Kap Ahn
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Abstract

Given a set $P$ of $n$ points in the plane and a multiset $W$ of $k$ weights with $k\leq n$, we assign each weight in $W$ to a distinct point in $P$ to minimize the maximum weighted distance from the weighted center of $P$ to any point in $P$. In this paper, we give two algorithms which take $O(k^2n^2\log^3 n)$ time and $O(k^5n\log^3k+kn\log^3 n)$ time, respectively. For a constant $k$, the second algorithm takes only $O(n\log^3n)$ time, which is near linear.

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Eunjin Oh, Hee-Kap Ahn. 2018-04-01. Assigning Weights to Minimize the Covering Radius in the Plane. https://arxiv.org/abs/1804.00241

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