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Online routing and searching on graphs with blocked edges

Author

Listed:
  • Davood Shiri

    (University of Sheffield)

  • Hakan Tozan

    (Istanbul Medipol University)

Abstract

We study routing and searching decisions of a search-and-detection (SDT) team on a road network under online uncertainty setting. Given an undirected edge-weighted bounded graph, a static target is positioned at an unknown vertex among potential target vertices in the graph. A non-negative search cost is given on each of the potential target vertices. The target is detected once the SDT searches its corresponding vertex. There may be some non-recoverable online blockages in the graph, but the existence of blockages is unknown to the SDT initially. If a blockage exists in the graph, it is disclosed online once the SDT visits one of its end-vertices. The graph stays connected when the blockages are omitted from it. The SDT begins from a certain vertex and aims to identify a route without any blocked edges which detects the target with minimum total traveling and search cost. We analyze this problem from a competitive analysis perspective under two scenarios with and without blockages. For the scenario with blockages, we provide a tight lower bound on the competitive ratio of deterministic solutions, an optimal deterministic solution, a randomized solution with a bounded expected competitive ratio, together with lower and upper bounds on the expected competitive ratio of the optimal randomized solutions. For the scenario without blockages, we provide tight lower bounds as well as optimal deterministic and randomized solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:2:d:10.1007_s10878-022-00876-9
    DOI: 10.1007/s10878-022-00876-9
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    References listed on IDEAS

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    1. Patrick Jaillet & Michael R. Wagner, 2006. "Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios," Transportation Science, INFORMS, vol. 40(2), pages 200-210, May.
    2. 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.
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    4. Patrick Jaillet & Michael R. Wagner, 2008. "Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses," Operations Research, INFORMS, vol. 56(3), pages 745-757, June.
    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. 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.
    7. 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.
    8. Davood Shiri & Vahid Akbari & F. Sibel Salman, 2020. "Online routing and scheduling of search-and-rescue teams," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(3), pages 755-784, September.
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    10. 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.
    11. 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.
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