The influence of maximum (s,t)-cuts on the competitiveness of deterministic strategies for the Canadian Traveller Problem

We study the k-Canadian Traveller Problem, where the objective is to lead a traveller in an undirected weighted graph G from a source s to a target t, knowing that at most k edges of the graph are blocked and cannot be traversed. The locations of blockages are unknown at the beginning of the walk but a blocked edge is revealed when the traveller visits one of its endpoints. There exist graphs for which the competitive ratio of any deterministic strategies cannot be smaller than 2k+1. Conversely, there exists a very simple strategy, reposition, which achieves this ratio 2k+1. It consists in successively traversing shortest (s,t)-paths and coming back to s when the traveller is blocked.