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The Shortlist Method for Fast Computation of the Earth Mover's Distance and Finding Optimal Solutions to Transportation Problems

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  • Carsten Gottschlich
  • Dominic Schuhmacher

Abstract

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.

Suggested Citation

  • Carsten Gottschlich & Dominic Schuhmacher, 2014. "The Shortlist Method for Fast Computation of the Earth Mover's Distance and Finding Optimal Solutions to Transportation Problems," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-10, October.
    • Handle: RePEc:plo:pone00:0110214
    DOI: 10.1371/journal.pone.0110214
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    References listed on IDEAS

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    Cited by:

    1. Espen Bernton & Pierre E. Jacob & Mathieu Gerber & Christian P. Robert, 2019. "Approximate Bayesian computation with the Wasserstein distance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 235-269, April.
    2. Filippo Zanetti & Jacek Gondzio, 2023. "An Interior Point–Inspired Algorithm for Linear Programs Arising in Discrete Optimal Transport," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1061-1078, September.
    3. Florian Ziel, 2020. "The energy distance for ensemble and scenario reduction," Papers 2005.14670, arXiv.org, revised Oct 2020.
    4. Carsten Gottschlich, 2016. "Convolution Comparison Pattern: An Efficient Local Image Descriptor for Fingerprint Liveness Detection," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-12, February.

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