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Constrained Two-Line Center Problems

Authors Taehoon Ahn , Sang Won Bae

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Author Details

Taehoon Ahn
  • Graduate School of Artificial Intelligence, Pohang University of Science and Technology, Republic of Korea
Sang Won Bae
  • Division of Artificial Intelligence and Computer Science, Kyonggi University, Suwon, Republic of Korea

Funding

  • Ahn, Taehoon: Supported by the Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (No. 2019-0-01906).
  • Bae, Sang Won: Supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2023-00251168).

Cite As Get BibTex

Taehoon Ahn and Sang Won Bae. Constrained Two-Line Center Problems. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.5

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(n² log² 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(n log n) time when the orientations of both lines are fixed; in O(n log³ n) time when the orientation of one line is fixed; and in O(n² α(n) log n) time when the angle between the two lines is fixed, where α(n) denotes the inverse Ackermann function.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • two-line center problem
  • geometric location problem
  • geometric optimization

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References

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