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The k-Canadian Travelers Problem with communication

Author

Listed:
  • Huili Zhang

    (Xi’an JiaoTong University
    State Key Lab for Manufacturing Systems Engineering
    Ministry of Education Key Lab for Process Control & Efficiency Engineering)

  • Yinfeng Xu

    (Xi’an JiaoTong University
    State Key Lab for Manufacturing Systems Engineering
    Ministry of Education Key Lab for Process Control & Efficiency Engineering)

  • Lan Qin

    (Xi’an JiaoTong University
    State Key Lab for Manufacturing Systems Engineering
    Ministry of Education Key Lab for Process Control & Efficiency Engineering)

Abstract

This paper studies a variation of the online k-Canadian Traveler Problem (k-CTP), in which there are multiple travelers who can communicate with each other, to share real-time blockage information of the edges. We study two different communication levels for the problem, complete communication (where all travelers can receive and send blockage information with each other) and limited communication (where only some travelers can both receive and send information while the others can only receive information). The objective is that at least one traveler finds a feasible route from the origin to the destination with as small cost as possible. We give lower bounds on the competitive ratio for both the two communication levels. Considering the urban traffic environment, we propose the Retrace-Alternating strategy and Greedy strategy for both the two communication levels, and prove that increasing the number of travelers with complete communication ability may not always improve the competitive ratio of online strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:2:d:10.1007_s10878-012-9503-x
    DOI: 10.1007/s10878-012-9503-x
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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 & 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. Huili Zhang & Yinfeng Xu & Xingang Wen, 2015. "Optimal shortest path set problem in undirected graphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 511-530, April.
    3. 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.
    4. 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.
    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. Lan Qin & Yinfeng Xu, 2017. "Fibonacci helps to evacuate from a convex region in a grid network," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 398-413, August.
    8. 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.
    9. Huili Zhang & Yinfeng Xu, 2018. "Online covering salesman problem," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 941-954, April.
    10. Yinfeng Xu & Huili Zhang, 2015. "How much the grid network and rescuers’ communication can improve the rescue efficiency in worst-case analysis," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1062-1076, November.

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