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arXiv · 2409.13304

Constrained Two-Line Center Problems

Taehoon Ahn·Sang Won Bae
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Abstract

Given a set P of n points in the plane, the two-line center problem asks to find two lines that minimize the maximum distance from each point in P to its closer one of the two resulting lines. The currently best algorithm for the problem takes $O(n^2\log^2n)$ time by Jaromczyk and Kowaluk in 1995. In this paper, we present faster algorithms for three variants of the two-line center problem in which the orientations of the resulting lines are constrained. Specifically, our algorithms solve the problem in $O(n \log n)$ time when the orientations of both lines are fixed; in $O(n \log^3 n)$ time when the orientation of one line is fixed; and in $O(n^2 α(n) \log n)$ time when the angle between the two lines is fixed, where $α(n)$ denotes the inverse Ackermann function.

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Taehoon Ahn, Sang Won Bae. 2024-09-20. Constrained Two-Line Center Problems. https://arxiv.org/abs/2409.13304

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