Spectrum Graph Coloring and Applications to Wi-Fi Channel Assignment

• Published in: Symmetry (Basel) 2018-03, Vol.10 (3), p.65
• Main Authors: Orden, David, Gimenez-Guzman, Jose, Marsa-Maestre, Ivan, de la Hoz, Enrique
• Format: Article
• Language: English
• Subjects: chromatic number; DSATUR; frequency assignment; Graph coloring; Graphs; Interference; Upper bounds; Wi-Fi channel assignment
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym10030065

We introduce and explore a family of vertex-coloring problems, which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of interferences between each pair of colors, the Threshold Spectrum Coloring problem fixes the number of colors available and aims to minimize the interference threshold, i.e., the maximum of the interferences at the vertices. Conversely, the Chromatic Spectrum Coloring problem fixes a threshold and aims to minimize the number of colors for which respecting that threshold is possible. As the main theoretical results, we prove tight upper bounds for the solutions to each problem. Since both problems turn out to be NP-hard, we complete the scene with experimental results. We propose a DSATUR-based heuristic and study its performance to minimize the maximum vertex interference in Wi-Fi channel assignment, both for randomly-generated graphs and for a real-world scenario. Further, for all these graphs, we experimentally check the goodness of the theoretical bounds.