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The canadian traveller problem and its competitive analysis

Author

Listed:
  • Yinfeng Xu

    (Xi’an Jiaotong University
    The State Key Lab for Manufacturing Systems Engineering)

  • Maolin Hu

    (Guyuan Teachers College)

  • Bing Su

    (Xi’an Jiaotong University
    The State Key Lab for Manufacturing Systems Engineering)

  • Binhai Zhu

    (Montana State University)

  • Zhijun Zhu

    (Xi’an Jiaotong University)

Abstract

From the online point of view, we study the Canadian Traveller Problem (CTP), in which the traveller knows in advance the structure of the graph and the costs of all edges. However, some edges may fail and the traveller only observes that upon reaching an adjacent vertex of the blocked edge. The goal is to find the least-cost route from the source O to the destination D, more precisely, to find an adaptive strategy minimizing the competitive ratio, which compares the performance of this strategy with that of a hypothetical offline algorithm that knows the entire topology in advance. In this paper, we present two adaptive strategies—a greedy or myopic strategy and a comparison strategy combining the greedy strategy and the reposition strategy in which the traveller backtracks to the source every time when he/she sees a failed edge. We prove tight competitive ratios of 2 k+1−1 and 2k+1 respectively for the two strategies, where k is the number of failed edges in the graph. Finally, we propose an explanation of why the greedy strategy and the comparison strategy are usually preferred by drivers in an urban traffic environment, based on an argument related to the length of the second-shortest path in a grid graph.

Suggested Citation

  • Yinfeng Xu & Maolin Hu & Bing Su & Binhai Zhu & Zhijun Zhu, 2009. "The canadian traveller problem and its competitive analysis," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 195-205, August.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:2:d:10.1007_s10878-008-9156-y
    DOI: 10.1007/s10878-008-9156-y
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    Citations

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    Cited by:

    1. Yinfeng Xu & Huili Zhang, 2015. "How much the grid network and rescuers’ communication can improve the rescue efficiency in worst-case analysis," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1062-1076, November.
    2. Sahin, Halenur & Kara, Bahar Yetis & Karasan, Oya Ekin, 2016. "Debris removal during disaster response: A case for Turkey," Socio-Economic Planning Sciences, Elsevier, vol. 53(C), pages 49-59.
    3. Huili Zhang & Yinfeng Xu & Xingang Wen, 2015. "Optimal shortest path set problem in undirected graphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 511-530, April.
    4. Davood Shiri & F. Sibel Salman, 2019. "On the randomized online strategies for the k-Canadian traveler problem," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 254-267, July.
    5. Marco Bender & Stephan Westphal, 2015. "An optimal randomized online algorithm for the $$k$$ k -Canadian Traveller Problem on node-disjoint paths," Journal of Combinatorial Optimization, Springer, vol. 30(1), pages 87-96, July.
    6. Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.
    7. Huili Zhang & Yinfeng Xu & Lan Qin, 2013. "The k-Canadian Travelers Problem with communication," Journal of Combinatorial Optimization, Springer, vol. 26(2), pages 251-265, August.
    8. Madhushini Narayana Prasad & Nedialko Dimitrov & Evdokia Nikolova, 2023. "Non-Aggressive Adaptive Routing in Traffic," Mathematics, MDPI, vol. 11(17), pages 1-25, August.
    9. Azadeh Tabatabaei & Mohammad Ghodsi, 2015. "Walking in streets with minimal sensing," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 387-401, August.
    10. Vural Aksakalli & O. Furkan Sahin & Ibrahim Ari, 2016. "An AO* Based Exact Algorithm for the Canadian Traveler Problem," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 96-111, February.
    11. Vural Aksakalli & Ibrahim Ari, 2014. "Penalty-Based Algorithms for the Stochastic Obstacle Scene Problem," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 370-384, May.
    12. Chung-Shou Liao & Yamming Huang, 2015. "Generalized Canadian traveller problems," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 701-712, May.
    13. Davood Shiri & F. Sibel Salman, 2017. "On the online multi-agent O–D k-Canadian Traveler Problem," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 453-461, August.
    14. Zhang, Huili & Tong, Weitian & Xu, Yinfeng & Lin, Guohui, 2015. "The Steiner Traveling Salesman Problem with online edge blockages," European Journal of Operational Research, Elsevier, vol. 243(1), pages 30-40.
    15. Davood Shiri & Hakan Tozan, 2022. "Online routing and searching on graphs with blocked edges," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1039-1059, September.

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