2018
A priori TSP in the scenario model
Publication
Publication
Discrete Applied Mathematics , Volume 250 p. 331- 341
In this paper, we consider the a priori traveling salesman problem 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.
| Additional Metadata | |
|---|---|
| , , , | |
| doi.org/10.1016/j.dam.2018.04.002 | |
| Discrete Applied Mathematics | |
| Organisation | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
|
van Ee, M., van Iersel, L., Janssen, T., & Sitters, R. (2018). A priori TSP in the scenario model. Discrete Applied Mathematics, 250, 331–341. doi:10.1016/j.dam.2018.04.002 |
|
