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