Approximating the Canadian Traveller Problem with Online Randomization

In this paper, we study online algorithms for the Canadian Traveller Problem defined by Papadimitriou and Yannakakis in 1991. This problem involves a traveller who knows entire road network advance, wishes to travel as quickly possible from source vertex s destination t, but discovers that some roads are blocked (e.g., snow) once reaching them. Achieving bounded competitive ratio is PSPACE-complete. Furthermore, if at most k can be blocked, optimal deterministic algorithm $$2k+1$$ , while only randomized result known so far lower bound of $$k+1$$ . We show, first time, polynomial time outperform best when there least two blockages, surpass an o(1) factor. Moreover, prove achieve $$\big (1+ \frac{\sqrt{2}}{2} \big )k + \sqrt{2}$$ pseudo-polynomial time. The proposed techniques also exploited implicitly represent multiple near-shortest s-t paths.