ScholarWorks@숙명여자대학교

초록

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(n2log2⁡n) 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(nlog⁡n) time when the orientations of both lines are fixed; in O(nlog3⁡n) time when the orientation of one line is fixed; and in O(n2α(n)log⁡n) time when the angle between the two lines is fixed, where α(n) denotes the inverse Ackermann function. © 2026 Elsevier B.V.

키워드