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Frequency assignment problem in networks with limited spectrum

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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.

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Authors and Affiliations

  1. School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China

    Zehui Shao

  2. Research Institute of Big Data, Chengdu University, Chengdu, 610106, China

    Zehui Shao

  3. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia

    Aleksander Vesel

  4. School of Electronic Engineering and Computer Science, Peking University, Beijing, 100871, China

    Jin Xu

Authors
  1. Zehui Shao
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  2. Aleksander Vesel
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  3. Jin Xu
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Corresponding author

Correspondence to Aleksander Vesel.

Additional information

This project is supported by the National Natural Science Foundation of China under Grant 61309015, the Ministry of Science of Slovenia under the Grant 0101-P-297, the National Basic Research Program of China (973 Program) Grant Nos. 2013CB329601 and 2013CB329603.

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Shao, Z., Vesel, A. & Xu, J. Frequency assignment problem in networks with limited spectrum. Cent Eur J Oper Res 25, 699–723 (2017). https://doi.org/10.1007/s10100-016-0462-7

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  • DOI: https://doi.org/10.1007/s10100-016-0462-7

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