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A priori TSP in the Scenario Model

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Approximation and Online Algorithms (WAOA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10138))

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Abstract

In this paper, we consider the a priori traveling salesman problem (TSP) in the scenario model. In this problem, we are given a list of subsets of the vertices, called scenarios, along with a probability for each scenario. Given a tour on all vertices, the resulting tour for a given scenario is obtained by restricting the solution to the vertices of the scenario. The goal is to find a tour on all vertices that minimizes the expected length of the resulting restricted tour. We show that this problem is already NP-hard and APX-hard when all scenarios have size four. On the positive side, we show that there exists a constant-factor approximation algorithm in three restricted cases: if the number of scenarios is fixed, if the number of missing vertices per scenario is bounded by a constant, and if the scenarios are nested. Finally, we discuss an elegant relation with an a priori minimum spanning tree problem.

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Acknowledgments

We would like to thank Karen Aardal, Jan Driessen and Neil Olver for useful discussions. A part of the work by Teun Janssen has been performed in the project INTEGRATE “Integrated Solutions for Agile Manufacturing in High-mix Semiconductor Fabs”, co-funded by grants from France, Italy, Ireland, The Netherlands and the ECSEL Joint Undertaking. Martijn van Ee and René Sitters are supported by the NWO Grant 612.001.215. Leo van Iersel was partially supported by NWO and partially by the 4TU Applied Mathematics Institute.

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Authors and Affiliations

  1. Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Martijn van Ee & René Sitters

  2. Delft University of Technology, Delft, The Netherlands

    Leo van Iersel & Teun Janssen

  3. Centrum voor Wiskunde en Informatica (CWI), Amsterdam, The Netherlands

    René Sitters

Authors
  1. Martijn van Ee
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  2. Leo van Iersel
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  3. Teun Janssen
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  4. René Sitters
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Correspondence to Martijn van Ee .

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Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität, Kiel, Germany

    Klaus Jansen

  2. Istituto Dalle Molle di Studi sull’ Intelligenza Artificiale, Manno (Lugano), Switzerland

    Monaldo Mastrolilli

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van Ee, M., van Iersel, L., Janssen, T., Sitters, R. (2017). A priori TSP in the Scenario Model. In: Jansen, K., Mastrolilli, M. (eds) Approximation and Online Algorithms. WAOA 2016. Lecture Notes in Computer Science(), vol 10138. Springer, Cham. https://doi.org/10.1007/978-3-319-51741-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-51741-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51740-7

  • Online ISBN: 978-3-319-51741-4

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