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An Experimental Study of Algorithms for Geodesic Shortest Paths in the Constant-Workspace Model

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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

We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed at random. In addition, the algorithm may use a constant number of words for reading and for writing. The constant-workspace model has been studied extensively in recent years, and algorithms for geodesic shortest paths have received particular attention.

We have implemented three such algorithms in Python, and we compare them to the classic algorithm by Lee and Preparata that uses linear time and linear space. We also clarify a few implementation details that were missing in the original description of the algorithms. Our experiments show that all algorithms perform as advertised in the original works and according to the theoretical guarantees. However, the constant factors in the running times turn out to be rather large for the algorithms to be fully useful in practice.

Supported in part by DFG projects MU/3501-1 and RO/2338-6 and ERC StG 757609.

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Notes

  1. 1.

    If a triangulation of P is already available, the implementation is relatively straightforward. If not, a linear-time implementation of the triangulation procedure constitutes a significant challenge [8]. Simpler methods are available, albeit at the cost of a slightly increased running time of \(O(n \log n)\) [7].

  2. 2.

    https://github.com/jonasc/constant-workspace-algos.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takustr. 9, 14195, Berlin, Germany

    Jonas Cleve & Wolfgang Mulzer

Authors
  1. Jonas Cleve
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  2. Wolfgang Mulzer
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Corresponding author

Correspondence to Jonas Cleve .

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

A Tables of Experimental Results

A Tables of Experimental Results

Here we list the experimental results shown in Figs. 7 and 8 (Tables 1 and 2).

Table 1. The median and maximum memory usage in bytes for all runs with a specific number of vertices n.
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Table 2. The median and maximum running times in seconds for all runs with a specific number of vertices n.
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Cleve, J., Mulzer, W. (2019). An Experimental Study of Algorithms for Geodesic Shortest Paths in the Constant-Workspace Model. 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_21

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  • DOI: https://doi.org/10.1007/978-3-030-34029-2_21

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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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