A priori TSP in the Scenario Model

Martijn van Ee, Leo van Iersel, Teun Janssen, R.A. Sitters

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

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.
Original languageEnglish
Title of host publicationApproximation and Online Algorithms
EditorsKlaus Jansen, Monaldo Mastrolilli
Place of PublicationCham
PublisherSpringer International Publishing
Pages183-196
Number of pages14
ISBN (Print)978-3-319-51741-4
Publication statusPublished - 2017

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