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On the randomized online strategies for the k-Canadian traveler problem

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  • Davood Shiri

    (Koc University)

  • F. Sibel Salman

    (Koc University)

Abstract

We consider the online k-Canadian Traveler Problem (k-CTP) which is defined on an undirected graph with a given source node O and a destination node D. Non-negative edge costs are given. The traveling agent is initially at O. There are k blocked edges in the graph, but these edges are not known to the agent. A blocked edge is learned when the agent arrives at one of its end-nodes. The goal of the agent is to arrive at D with minimum total cost. We consider the k-CTP on graphs that consist of only node-disjoint O–D paths, where it was shown that there is no randomized online strategy with competitive ratio better than $$k+1$$ k + 1 . An optimal randomized online strategy was also given. However, we prove that the given strategy cannot be implemented in some cases. We also modify the given strategy such that it can be implemented in all cases and meets the lower bound of $$k+1$$ k + 1 .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-019-00378-1
    DOI: 10.1007/s10878-019-00378-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Chung-Shou Liao & Yamming Huang, 2015. "Generalized Canadian traveller problems," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 701-712, May.
    5. 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.
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    Cited by:

    1. Akbari, Vahid & Shiri, Davood & Sibel Salman, F., 2021. "An online optimization approach to post-disaster road restoration," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 1-25.
    2. Akbari, Vahid & Shiri, Davood, 2021. "Weighted online minimum latency problem with edge uncertainty," European Journal of Operational Research, Elsevier, vol. 295(1), pages 51-65.
    3. 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.
    4. Davood Shiri & Vahid Akbari, 2021. "Online Failure Diagnosis in Interdependent Networks," SN Operations Research Forum, Springer, vol. 2(1), pages 1-14, March.

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