Article Dans Une Revue Journal of Combinatorial Optimization Année : 2019

Multiple Canadians on the road: minimizing the distance competitive ratio

Résumé

The online k-Canadian Traveller Problem (k-CTP), known to be PSPACE-complete, asks for the best strategy a traveller has to follow in order to traverse with minimum distance a graph from s to t where at most k edges are blocked. A blocked edge is revealed when the traveller visits one of its endpoints. It is proven that for any deterministic strategy, the competitive ratio is larger than 2k + 1. Indeed, the distance traversed by the traveller is potentially greater than 2k + 1 times the optimal journey. For randomized strategies, this ratio becomes k + 1. We complement the work of Zhang et al. on k-CTP with multiple travellers by evaluating the distance competitive ratio of deterministic and randomized strategies for complete and partial communication. We compare these ratios with two other communication levels: when travellers do not communicate at all and when they communicate only before beginning to move. Eventually, we provide a wide picture of the distance competitiveness reachable for the k-CTP in function of the number of travellers and communication levels.

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Dates et versions

hal-02343983 , version 1 (03-11-2019)

Identifiants

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Pierre Bergé, Jean Desmarchelier, Wen Guo, Aurélie Lefebvre, Arpad Rimmel, et al.. Multiple Canadians on the road: minimizing the distance competitive ratio. Journal of Combinatorial Optimization, 2019, 38 (4), pp.1086-1100. ⟨10.1007/s10878-019-00438-6⟩. ⟨hal-02343983⟩
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