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An optimal randomized online algorithm for the $$k$$ k -Canadian Traveller Problem on node-disjoint paths

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  • Marco Bender

    (University of Göttingen)

  • Stephan Westphal

    (University of Göttingen)

Abstract

We consider the $$k$$ k -Canadian Traveller Problem, which asks for a shortest path between two nodes $$s$$ s and $$t$$ t in an undirected graph, where up to $$k$$ k edges may be blocked. An online algorithm learns about a blocked edge when reaching one of its endpoints. Recently, it has been shown that no randomized online algorithm can be better than $$(k+1)$$ ( k + 1 ) -competitive, even if all $$s$$ s - $$t$$ t -paths are node-disjoint. We show that the bound is tight by constructing a randomized online algorithm for this case that achieves the ratio against an oblivious adversary and is therefore best possible.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:1:d:10.1007_s10878-013-9634-8
    DOI: 10.1007/s10878-013-9634-8
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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.
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    Cited by:

    1. 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.
    2. Pierre Bergé & Jean Desmarchelier & Wen Guo & Aurélie Lefebvre & Arpad Rimmel & Joanna Tomasik, 2019. "Multiple Canadians on the road: minimizing the distance competitive ratio," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1086-1100, November.
    3. Davood Shiri & Vahid Akbari, 2021. "Online Failure Diagnosis in Interdependent Networks," SN Operations Research Forum, Springer, vol. 2(1), pages 1-14, March.
    4. Davood Shiri & F. Sibel Salman, 2019. "Competitive analysis of randomized online strategies for the multi-agent k-Canadian Traveler Problem," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 848-865, April.
    5. 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.
    6. 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.
    7. 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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