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Online minimum latency problem with edge uncertainty

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

Abstract

Given a tour in a metric space, the latency of the vertex v is the distance traveled along the tour starting from the root and arriving at v for the first time. The minimum latency problem (MLP) is to find a tour visiting all given vertices such that the total latency of these vertices is minimized. We consider an online variant in traffic networks, where as many as ℓ edges are to be blocked during the traversal, for a non-negative integer ℓ. We first prove a lower bound on the competitive ratio for any online algorithm and then propose an online algorithm GoodTreeTraversal, which is demonstrated to be near optimal if there is a good k-tree for every k in the range from 2 to n and the number of blockages is large enough. We also present a polynomial time heuristic algorithm called Detour, which is much faster than GoodTreeTraversal. The numerical experiments demonstrate the efficiency and effectiveness of our two algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:2:p:418-429
    DOI: 10.1016/j.ejor.2018.08.017
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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. 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.
    3. 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.
    4. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    5. Matteo Fischetti & Gilbert Laporte & Silvano Martello, 1993. "The Delivery Man Problem and Cumulative Matroids," Operations Research, INFORMS, vol. 41(6), pages 1055-1064, December.
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    Cited by:

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    5. Zweigle, Tanja & Hellinghausen, Paul, 2021. "Relevanz und Potential von TikTok für die Social-Media-Marketing-Strategie von Unternehmen," IU Discussion Papers - Marketing & Communication 01 (Dez. 2021), IU International University of Applied Sciences.
    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. Kühn, Frauke & Lichters, Marcel & Krey, Nina, 2020. "The touchy issue of produce: Need for touch in online grocery retailing," Journal of Business Research, Elsevier, vol. 117(C), pages 244-255.
    8. 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.
    9. Denk, Maximilian & Khabyuk, Olexiy, "undated". "Wie relevant sind Chatbots als Kommunikations- und Marketinginstrument für Hochschulen? Konzeption und Akzeptanz eines Chatbot-Prototyps für den Master-Studiengang „Kommunikations-, Multimedia- und Ma," Duesseldorf Working Papers in Applied Management and Economics 52, Duesseldorf University of Applied Sciences.

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