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- W2809282601 abstract "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." @default.
- W2809282601 created "2018-06-29" @default.
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- W2809282601 date "2018-12-01" @default.
- W2809282601 modified "2023-10-03" @default.
- W2809282601 title "A priori TSP in the scenario model" @default.
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- W2809282601 doi "https://doi.org/10.1016/j.dam.2018.04.002" @default.
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