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Using Laplacian Eigenvalues and Eigenvectors in the Analysis of Frequency Assignment Problems.

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Title: Using Laplacian Eigenvalues and Eigenvectors in the Analysis of Frequency Assignment Problems.
Authors: Van Den Heuvel, Jan1 jan@maths.lse.ac.uk, Snežana Pejić1
Source: Annals of Operations Research. 2001, Vol. 107 Issue 1-4, p349-368. 20p. 5 Graphs.
Subjects: Assignment problems (Programming), Nonlinear assignment problems, Radio frequency, Radio transmitter-receivers, Laplacian operator, Matrices (Mathematics), Eigenvalues, Operations research
Abstract: A Frequency Assignment Problem (FAP) is the problem that arises when frequencies have to be assigned to a given set of transmitters so that spectrum is used efficiently and the interference between the transmitters is minimal. In this paper we see the frequency assignment problem as a generalised graph colouring problem, where transmitters are presented by vertices and interaction between two transmitters by a weighted edge. We generalise some properties of Laplacian matrices that hold for simple graphs. We investigate the use of Laplacian eigenvalues and eigenvectors as tools in the analysis of properties of a FAP and its generalised chromatic number (the so-called span). [ABSTRACT FROM AUTHOR]
Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Frequency Assignment Problem (FAP) is the problem that arises when frequencies have to be assigned to a given set of transmitters so that spectrum is used efficiently and the interference between the transmitters is minimal. In this paper we see the frequency assignment problem as a generalised graph colouring problem, where transmitters are presented by vertices and interaction between two transmitters by a weighted edge. We generalise some properties of Laplacian matrices that hold for simple graphs. We investigate the use of Laplacian eigenvalues and eigenvectors as tools in the analysis of properties of a FAP and its generalised chromatic number (the so-called span). [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1023/A:1014927805247
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        Text: English
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        Type: general
      – SubjectFull: Nonlinear assignment problems
        Type: general
      – SubjectFull: Radio frequency
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      – SubjectFull: Radio transmitter-receivers
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      – SubjectFull: Laplacian operator
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      – SubjectFull: Matrices (Mathematics)
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      – SubjectFull: Eigenvalues
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              Text: 2001
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