Multiple Canadians on the road: minimizing the distance competitive ratio

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.