Spectrum graph coloring and applications to WiFi channel assignment

TL;DR

This paper introduces new vertex-coloring problems inspired by Wi-Fi channel assignment, providing theoretical bounds, proving NP-hardness, and proposing heuristics with experimental validation on real-world and synthetic graphs.

Contribution

It defines and analyzes two novel spectrum coloring problems related to Wi-Fi interference, establishing tight bounds, proving NP-hardness, and developing heuristics with experimental evaluation.

Findings

Proved tight upper bounds for the new coloring problems

Demonstrated NP-hardness of both problems

Validated heuristic performance on real-world and synthetic graphs

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.