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The Steiner Traveling Salesman Problem with online edge blockages

Author

Listed:
  • Zhang, Huili
  • Tong, Weitian
  • Xu, Yinfeng
  • Lin, Guohui

Abstract

We consider the online Steiner Traveling Salesman Problem. In this problem, we are given an edge-weighted graph G = (V, E) and a subset D⊆V of destination vertices, with the optimization goal to find a minimum weight closed tour that traverses every destination vertex of D at least once. During the traversal, the salesman could encounter at most k non-recoverable blocked edges. The edge blockages are real-time, meaning that the salesman knows about a blocked edge whenever it occurs. We first show a lower bound on the competitive ratio and present an online optimal algorithm for the problem. While this optimal algorithm has non-polynomial running time, we present another online polynomial-time near optimal algorithm for the problem. Experimental results show that our online polynomial-time algorithm produces solutions very close to the offline optimal solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:1:p:30-40
    DOI: 10.1016/j.ejor.2014.11.013
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Shanxiu Jiang & Li Luo, 2019. "Online in-time service problem with minimal server assignment," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 114-122, January.
    5. Huili Zhang & Yinfeng Xu, 2018. "Online covering salesman problem," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 941-954, April.
    6. 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.
    7. 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.
    8. Zhang, Huili & Tong, Weitian & Lin, Guohui & Xu, Yinfeng, 2019. "Online minimum latency problem with edge uncertainty," European Journal of Operational Research, Elsevier, vol. 273(2), pages 418-429.
    9. 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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