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Frequency assignment problem in networks with limited spectrum

Author

Listed:
  • Zehui Shao

    (Chengdu University
    Chengdu University)

  • Aleksander Vesel

    (University of Maribor)

  • Jin Xu

    (Peking University)

Abstract

The frequency assignment problem (FAP) asks for assigning frequencies (channels) in a wireless network from the available radio spectrum to the transceivers of the network. One of the graph theoretical models of FAP is the L(3, 2, 1)-labeling of a graph, which is an abstraction of assigning integer frequencies to radio transceivers such that (i) transceivers that are one unit of distance apart receive frequencies that differ by at least three, (ii) transceivers that are two units of distance apart receive frequencies that differ by at least two, and (iii) transceivers that are three units of distance apart receive frequencies that differ by at least one. The relaxation of the L(3, 2, 1)-labeling called the (s, t, r)-relaxed k-L(3, 2, 1)-labeling is proposed in this paper. This concept is a generalization of the (s, t)-relaxed k-L(2, 1)-labeling (Lin in J Comb Optim 2016, doi: 10.1007/s10878-014-9746-9 ). Basic properties of (s, t, r)-relaxed k-L(3, 2, 1)-labeling are discussed and optimal (s, t, r)-relaxed k-L(3, 2, 1)-labelings for paths and some cycles as well as for the hexagonal lattice and the square lattice are determined.

Suggested Citation

  • Zehui Shao & Aleksander Vesel & Jin Xu, 2017. "Frequency assignment problem in networks with limited spectrum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(3), pages 699-723, September.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:3:d:10.1007_s10100-016-0462-7
    DOI: 10.1007/s10100-016-0462-7
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    References listed on IDEAS

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    1. Georgy Zadonsky, 2015. "Ипотека В Рф," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 2, pages 35-36, Февраль.
    2. Georgy Zadonsky, 2015. "Рынок Недвижимости Рф," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 3, pages 33-35, Март.
    3. Dupont, Audrey & Linhares, Andréa Carneiro & Artigues, Christian & Feillet, Dominique & Michelon, Philippe & Vasquez, Michel, 2009. "The dynamic frequency assignment problem," European Journal of Operational Research, Elsevier, vol. 195(1), pages 75-88, May.
    4. Nikita Andrievskiy & Elizaveta Khudko, 2015. "Финансовые Рынки," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 3, pages 13-17, Март.
    5. Nadezhda Volovik, 2015. "Внешняя Торговля," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 1, pages 27-29, Январь.
    6. Georgy Zadonsky, 2015. "Рынок Недвижимости Рф," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 1, pages 38-41, Январь.
    7. Nadezhda Volovik, 2015. "Внешняя Торговля," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 2, pages 22-25, Февраль.
    8. Nadezhda Volovik, 2015. "Внешняя Торговля," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 3, pages 29-32, Март.
    9. Nikita Andrievskiy, 2015. "Финансовые Рынки," Russian Economic Development (in Russian), Gaidar Institute for Economic Policy, issue 1, pages 12-15, Январь.
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    Cited by:

    1. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 773-790, September.

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