Node coloring in wireless networks: Complexity results and grid coloring

Coloring is used in wireless networks to improve communication efficiency, mainly in terms of bandwidth, energy and possibly end-to-end delays. In this paper, we define the h-hop node coloring problem, with h any positive integer, adapted to two types of applications in wireless networks. We specify coloring in both general mode for general applications and strategic mode for data gathering applications. We prove that the associated decision problem is NP-complete. We focus on grid topologies considering small or large node densities. We present a coloring method that determines a color pattern for various transmission ranges, and color the grid by tiling this color pattern. We prove that this method produces the optimal number of colors. The coloring results are then compared to those obtained by a 3-hop distributed coloring algorithm, called SERENA. Through simulation results, we highlight the impact of node priority assignment on the number of colors obtained for any network and grids in particular. Based on these results, we identify directions to improve SERENA.