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Another Look at the Shoelace TSP: The Case of Very Old Shoes

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Fun with Algorithms (FUN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8496))

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Abstract

What is the most efficient way of lacing a shoe? Mathematically speaking, this question concerns the structure of certain special cases of the bipartite travelling salesman problem (BTSP).

We show that techniques developed for the analysis of the (standard) TSP may be applied successfully to characterize well-solvable cases of the BTSP and the shoelace problem. In particular, we present a polynomial time algorithm that decides whether there exists a renumbering of the cities such that the resulting distance matrix carries a benevolent combinatorial structure that allows one to write down the optimal solution without further analysis of input data. Our results generalize previously published well-solvable cases of the shoelace problem.

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Author information

Authors and Affiliations

  1. Warwick Business School, Coventry, United Kingdom

    Vladimir G. Deineko

  2. TU Eindhoven, Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Vladimir G. Deineko
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  2. Gerhard J. Woeginger
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Città Universitaria, Università degli Studi di Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Alfredo Ferro

  2. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Fabrizio Luccio

  3. Institute of Theoretical Computer Science, ETH Zürich, Universitätsstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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Deineko, V.G., Woeginger, G.J. (2014). Another Look at the Shoelace TSP: The Case of Very Old Shoes. In: Ferro, A., Luccio, F., Widmayer, P. (eds) Fun with Algorithms. FUN 2014. Lecture Notes in Computer Science, vol 8496. Springer, Cham. https://doi.org/10.1007/978-3-319-07890-8_11

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  • DOI: https://doi.org/10.1007/978-3-319-07890-8_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07889-2

  • Online ISBN: 978-3-319-07890-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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