Spectrum graph coloring and applications to WiFi channel assignment

Motivated by WiFi channel assignment, we propose and explore two vertex-coloring problems for graphs, where the spectrum of colors is endorsed 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. The Chromatic Spectrum Coloring problem fixes a threshold and aims to minimize the number of colors for which respecting that threshold is possible. As theoretical results, we show that both problems are NP-hard and we prove upper bounds for the solutions to each problem, with interesting applications to the design and planning of wireless network infrastructures. We complete the scene with experimental results, proposing a DSATUR-based heuristic for each problem and comparing them with the nonlinear optimizer ALHSO.