A priori TSP in the Scenario Model

  • Martijn van Ee
  • Leo van Iersel
  • Teun Janssen
  • René Sitters
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10138)


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.


Traveling salesman problem A priori optimization Master tour Optimization under scenarios 



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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Martijn van Ee
    • 1
  • Leo van Iersel
    • 2
  • Teun Janssen
    • 2
  • René Sitters
    • 1
    • 3
  1. 1.Vrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Delft University of TechnologyDelftThe Netherlands
  3. 3.Centrum voor Wiskunde en Informatica (CWI)AmsterdamThe Netherlands

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