Spectrum graph coloring and applications to WiFi channel assignment

Abstract

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 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.

28 pages, 7 figures, 11 tables, submitted. From the previous version, more experiments have been added and some rephrasing performed

References in corpus (1)

• A DSATUR-based algorithm for the Equitable Coloring Problem

Cited by in corpus (3)

• Nonlinear Negotiation Approaches for Complex-Network Optimization: A Study Inspired by Wi-Fi Channel Assignment
• Spectrum graph coloring to improve Wi-Fi channel assignment in a real-world scenario via edge contraction
• REACT: REActive resilience for critical infrastructures using graph-Coloring Techniques