Frequency assignment problem in networks with limited spectrum

Frequency assignment problem in networks with limited spectrum

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Article ID: iaor20173352
Volume: 25
Issue: 3
Start Page Number: 699
End Page Number: 723
Publication Date: Sep 2017
Journal: Central European Journal of Operations Research
Authors:
Keywords: combinatorial optimization, networks, graphs, heuristics, programming: integer
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 kL(3, 2, 1)‐labeling is proposed in this paper. This concept is a generalization of the (s, t)‐relaxed kL(2, 1)‐labeling (Lin in J Comb Optim 2016, doi: 10.1007/s10878-014-9746-9). Basic properties of (s, t, r)‐relaxed kL(3, 2, 1)‐labeling are discussed and optimal (s, t, r)‐relaxed kL(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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