Node Coloring in Wireless Networks: Complexity Results and Grid Coloring

TL;DR

This paper investigates the complexity of node coloring in wireless networks, proves NP-completeness, and proposes optimal and distributed coloring algorithms for grid topologies, with simulations showing their effectiveness.

Contribution

It introduces the h-hop node coloring problem, proves its NP-completeness, and provides optimal grid coloring patterns along with a distributed algorithm, SERENA.

Findings

NP-complete decision problem for h-hop coloring

Optimal periodic coloring patterns for grid topologies

SERENA algorithm's performance depends on node priority

Abstract

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 both general mode for general applications and strategic mode for data gathering applications.We prove that the associated decision problem is NP-complete. We then focus on grid topologies that constitute regular topologies for large or dense wireless networks. We consider various transmission ranges and identify a color pattern that can be reproduced to color the whole grid with the optimal number of colors. We obtain an optimal periodic coloring of the grid for the considered transmission range. We then present 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. We then compare these optimal results on grids with those obtained by SERENA and identify directions to improve SERENA.