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Computing Balanced Convex Partitions of Lines

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LATIN 2020: Theoretical Informatics (LATIN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12118))

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Abstract

Dujmović and Langerman (2013) proved a ham-sandwich cut theorem for an arrangement of lines in the plane. Recently, Xue and Soberón (2019) generalized it to balanced convex partitions of lines in the plane. In this paper, we study the computational problems of computing a ham-sandwich cut balanced convex partitions for an arrangement of lines in the plane. We show that both problems can be solved in polynomial time.

The research is supported in part by NSF award CCF-1718994.

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Authors and Affiliations

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

    Sergey Bereg

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  1. Sergey Bereg
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Correspondence to Sergey Bereg .

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Editors and Affiliations

  1. University of São Paulo, São Paulo, Brazil

    Yoshiharu Kohayakawa

  2. University of Campinas, Campinas, Brazil

    Flávio Keidi Miyazawa

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Bereg, S. (2020). Computing Balanced Convex Partitions of Lines. In: Kohayakawa, Y., Miyazawa, F.K. (eds) LATIN 2020: Theoretical Informatics. LATIN 2021. Lecture Notes in Computer Science(), vol 12118. Springer, Cham. https://doi.org/10.1007/978-3-030-61792-9_20

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  • DOI: https://doi.org/10.1007/978-3-030-61792-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-61791-2

  • Online ISBN: 978-3-030-61792-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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