Abstract
The k-Canadian Traveller Problem (\(k\)-CTP), proven PSPACE-complete by Papadimitriou and Yannakakis, is a generalization of the Shortest Path Problem which admits blocked edges. Its objective is to determine the strategy that makes the traveller traverse graph G between two given nodes s and t with the minimal distance, knowing that at most k edges are blocked. The traveller discovers that an edge is blocked when arriving at one of its endpoints.
We study the competitiveness of randomized memoryless strategies to solve the \(k\)-CTP. Memoryless strategies are attractive in practice as a decision made by the strategy for a traveller in node v of G does not depend on his anterior moves. We establish that the competitive ratio of any randomized memoryless strategy cannot be better than \(2k + O\left( 1\right) \). This means that randomized memoryless strategies are asymptotically as competitive as deterministic strategies which achieve a ratio \(2k+1\) at best.
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Bergé, P., Hemery, J., Rimmel, A., Tomasik, J. (2018). On the Competitiveness of Memoryless Strategies for the k-Canadian Traveller Problem. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_38
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DOI: https://doi.org/10.1007/978-3-030-04651-4_38
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