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Approximating k-Orthogonal Line Center

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Combinatorial Optimization and Applications (COCOA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12577))

Abstract

k-orthogonal line center problem computes a set of k axis-parallel lines for a given set of n points such that the maximum among the distances between each point and its nearest line is minimized. In this paper, we design a deterministic bi-criteria approximation algorithm that runs in \(O(k^2n \log n)\) time and returns at most \(\frac{3}{2}k\) lines such that the minimized distance is within 16r. Here r is the minimized distance in the optimal solution with k line centers for the given input.

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Authors and Affiliations

  1. Ramakrishna Mission Vivekananda Educational and Research Institute, Howrah, India

    Barunabha Chakraborty & Joydeep Mukherjee

  2. Indian Statistical Institute, Kolkata, India

    Arun Kumar Das & Sandip Das

Authors
  1. Barunabha Chakraborty
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  2. Arun Kumar Das
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  3. Sandip Das
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  4. Joydeep Mukherjee
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Corresponding author

Correspondence to Arun Kumar Das .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Xiamen University, Xiamen, China

    Zhongnan Zhang

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Chakraborty, B., Das, A.K., Das, S., Mukherjee, J. (2020). Approximating k-Orthogonal Line Center. In: Wu, W., Zhang, Z. (eds) Combinatorial Optimization and Applications. COCOA 2020. Lecture Notes in Computer Science(), vol 12577. Springer, Cham. https://doi.org/10.1007/978-3-030-64843-5_4

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  • DOI: https://doi.org/10.1007/978-3-030-64843-5_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64842-8

  • Online ISBN: 978-3-030-64843-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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