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On Partitioning a Cake

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Discrete and Computational Geometry (JCDCG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2866))

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Abstract

We investigate balanced α-partitions of a generalized cake which has two masses, one distributed in a convex set and the other distributed on its boundary. We characterize all ratio vectors α such that any cake has a perfect α-partition. We also consider convex α-partitions of a cake into three pieces. It is known [4, 5, 9] that any two masses have convex α-partition for α=(1/3,1/3,1/3). We prove the existence of convex α-partitions for any α=(a,a,1-2a), 0<a<1/3. We also provide an infinite family of α each of which does not guarantee a convex α-partition of a cake.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, Box 830688, Richardson, TX, 75083, USA

    Sergei Bespamyatnikh

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  1. Sergei Bespamyatnikh
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Editors and Affiliations

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

    Jin Akiyama

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

    Mikio Kano

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© 2003 Springer-Verlag Berlin Heidelberg

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Bespamyatnikh, S. (2003). On Partitioning a Cake. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_7

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  • DOI: https://doi.org/10.1007/978-3-540-44400-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20776-4

  • Online ISBN: 978-3-540-44400-8

  • eBook Packages: Springer Book Archive

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