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A Faster Convex-Hull Algorithm via Bucketing

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Analysis of Experimental Algorithms (SEA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11544))

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Abstract

In the convex-hull problem, in two-dimensional space, the task is to find, for a given sequence S of n points, the smallest convex polygon for which each point of S is either in its interior or on its boundary. In this paper, we propose a variant of the classical bucketing algorithm that (1) solves the convex-hull problem for any multiset of points, (2) uses \(O(\sqrt{n}\,)\) words of extra space, (3) runs in O(n) expected time on points drawn independently and uniformly from a rectangle, and (4) requires \(O(n \lg {} n)\) time in the worst case. Also, we perform experiments to compare bucketing to other alternatives that are known to work in linear expected time. In our tests, in the integer-coordinate setting, bucketing was a clear winner compared to the considered competitors (plane-sweep, divide & conquer, quickhull, and throw-away).

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Author information

Authors and Affiliations

  1. National Space Institute, Technical University of Denmark, Centrifugevej, 2800, Kongens Lyngby, Denmark

    Ask Neve Gamby

  2. Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen East, Denmark

    Jyrki Katajainen

  3. Jyrki Katajainen and Company, 3390, Hundested, Denmark

    Jyrki Katajainen

Authors
  1. Ask Neve Gamby
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  2. Jyrki Katajainen
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Corresponding author

Correspondence to Jyrki Katajainen .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

  2. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  3. University of Ioannina, Ioannina, Greece

    Konstantinos E. Parsopoulos

  4. Delft University of Technology, Delft, The Netherlands

    Dimitris Souravlias

  5. University of Florida, Gainesville, FL, USA

    Arsenis Tsokas

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Gamby, A.N., Katajainen, J. (2019). A Faster Convex-Hull Algorithm via Bucketing. In: Kotsireas, I., Pardalos, P., Parsopoulos, K., Souravlias, D., Tsokas, A. (eds) Analysis of Experimental Algorithms. SEA 2019. Lecture Notes in Computer Science(), vol 11544. Springer, Cham. https://doi.org/10.1007/978-3-030-34029-2_30

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  • DOI: https://doi.org/10.1007/978-3-030-34029-2_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34028-5

  • Online ISBN: 978-3-030-34029-2

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