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Canadians Should Travel Randomly

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Book cover Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8572))

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Abstract

We study online algorithms for the Canadian Traveller Problem (CTP) introduced by Papadimitriou and Yannakakis in 1991. In this problem, a traveller 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. It is PSPACE-complete to achieve a bounded competitive ratio for this problem. Furthermore, if at most k roads can be blocked, then the optimal competitive ratio for a deterministic online algorithm is 2k + 1, while the only randomized result known is a lower bound of k + 1.

In this paper, we show for the first time that a polynomial time randomized algorithm can beat the best deterministic algorithms, surpassing the 2k + 1 lower bound by an o(1) factor. Moreover, we prove the randomized algorithm achieving a competitive ratio of \(\big(1+ \frac{\sqrt{2}}{2} \big)k +1\) in pseudo-polynomial time. The proposed techniques can also be applied to implicitly represent multiple near-shortest s-t paths.

Supported by NSC Grant 102-2221-E-007-075-MY3 and KAKENHI 23240002.

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Author information

Authors and Affiliations

  1. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Erik D. Demaine

  2. Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, 30013, Taiwan

    Yamming Huang & Chung-Shou Liao

  3. National Institute of Informatics, Tokyo, Japan

    Kunihiko Sadakane

Authors
  1. Erik D. Demaine
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  2. Yamming Huang
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  3. Chung-Shou Liao
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  4. Kunihiko Sadakane
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Elias Koutsoupias

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Demaine, E.D., Huang, Y., Liao, CS., Sadakane, K. (2014). Canadians Should Travel Randomly. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_32

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  • DOI: https://doi.org/10.1007/978-3-662-43948-7_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43947-0

  • Online ISBN: 978-3-662-43948-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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