Simple Distributed Δ + 1 Coloring in the SINR Model

In wireless ad hoc networks, distributed node coloring is a fundamental problem closely related to establishing efficient communication through TDMA schedules. For networks with maximum degree Δ, a Δ + 1 coloring is the ultimate goal in the distributed setting as this is always possible. In this work we propose a very simple 4Δ coloring along with a color reduction technique to achieve Δ + 1 colors. All algorithms have a runtime of \(\mathcal{O}(\Delta \log n)\) time slots. This improves on previous algorithms for the SINR model either in terms of the number of required colors or the runtime, and matches the runtime of local broadcasting in the SINR model (which can be seen as an asymptotical lower bound).