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Output-sensitive cell enumeration in hyperplane arrangements

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Algorithm Theory — SWAT'98 (SWAT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1432))

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Abstract

We present a simple and practical algorithm for enumerating the set of cells C of an arrangement of m hyperplanes. For fixed dimension its time complexity is O(m ίddot ¦ C ¦). This is an improvement by a factor of m over the reverse search algorithm by Avis and Fukuda. The algorithm needs little space, is output-sensitive, straightforward to parallelize and the implementation is simple for all dimensions.

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Authors and Affiliations

  1. Institut für Theoretische Informatik, ETH Zentrum, 8092, Zürich, Switzerland

    Nora Sleumer

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  1. Nora Sleumer
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Editor information

Stefan Arnborg Lars Ivansson

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© 1998 Springer-Verlag Berlin Heidelberg

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Sleumer, N. (1998). Output-sensitive cell enumeration in hyperplane arrangements. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054377

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  • DOI: https://doi.org/10.1007/BFb0054377

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64682-2

  • Online ISBN: 978-3-540-69106-8

  • eBook Packages: Springer Book Archive

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