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 \(2k+1\), while the only randomized result known so far is a lower bound of \(k+1\). 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 \(2k+1\) by an o(1) factor. Moreover, we prove that the randomized algorithm can achieve a competitive ratio of \(\big (1+ \frac{\sqrt{2}}{2} \big )k + \sqrt{2}\) in pseudo-polynomial time. The proposed techniques can also be exploited to implicitly represent multiple near-shortest s-t paths.

在本文中，我们研究了在线算法加拿大旅行者问题从源顶点尽快通过PAPADIMITRIOU和Yannakakis定义在1991年这个问题涉及到谁事先知道整个路网旅客，并希望行进小号的目的地顶点t，但在网上发现有些道路一到达便被阻塞（例如被雪）。实现该问题的有限竞争比率是PSPACE完全的。此外，如果最多只能阻塞k条道路，则确定性在线算法的最佳竞争比为\（2k + 1 \），而到目前为止已知的唯一随机结果是\（k + 1 \）的下限。我们首次证明，当存在至少两个障碍时，多项式时间随机算法可以胜过最佳确定性算法，并且将o（2k + 1 \）的下限超出o（1）倍。此外，我们证明了该随机算法在伪多项式时间内可以达到\（\ big（1+ \ frac {\ sqrt {2}} {2} \ big）k + \ sqrt {2} \）的竞争比。提出的技术也可以被利用来隐式地表示多个接近最短的s - t路径。