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)

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.

Keywords

Traveling salesman problem A priori optimization Master tour Optimization under scenarios 

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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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