Approximating the Discrete Center Line Segment in Linear Time.

Let P be a set of n points in the plane. The discrete center line segment of P is the line segment with both its endpoints in P such that the maximum distance from any point in P to it is minimized. In 2021, Daescu and Teo [6] gave a quadratic time algorithm using quadratic space. In this paper, we give a $$(1+\varepsilon )$$ -approximation algorithm for the problem which runs in $$O(n+\frac{1}{\varepsilon ^4}\log \frac{1}{\varepsilon })$$ time using linear space.