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Weighted Ham-Sandwich Cuts

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Discrete and Computational Geometry (JCDCG 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3742))

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Abstract

Let R and B be two sets of n points. A ham-sandwich cut is a line that simultaneously bisects R and B, and is known to always exist. This notion can be generalized to the case where each point p ∈ R ∪ B is associated with a weight w p . A ham-sandwich cut can still be proved to exist, even if weights are allowed to be negative. In this paper, we present a O(n log n) algorithm to find a weighted ham-sandwich cut, but we show that deciding whether that cut is unique is 3-SUM hard.

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Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, Canada

    Prosenjit Bose

  2. Département d’Informatique, Université Libre de Bruxelles, Belgium

    Stefan Langerman

Authors
  1. Prosenjit Bose
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  2. Stefan Langerman
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Mikio Kano

  3. Tokai University, 317 Nishino, 410-0395, Numazu, Japan

    Xuehou Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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Bose, P., Langerman, S. (2005). Weighted Ham-Sandwich Cuts. In: Akiyama, J., Kano, M., Tan, X. (eds) Discrete and Computational Geometry. JCDCG 2004. Lecture Notes in Computer Science, vol 3742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11589440_5

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  • DOI: https://doi.org/10.1007/11589440_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30467-8

  • Online ISBN: 978-3-540-32089-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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