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 language | English |
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Title of host publication | Approximation and Online Algorithms |
Editors | Klaus Jansen, Monaldo Mastrolilli |
Place of Publication | Cham |
Publisher | Springer International Publishing |
Pages | 183-196 |
Number of pages | 14 |
ISBN (Print) | 978-3-319-51741-4 |
Publication status | Published - 2017 |