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 \(2k+1\), 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
