Experimental Study of Independent and Dominating Sets in Wireless Sensor Networks Using Graph Coloring Algorithms

The domatic partition problem seeks to maximize the partitioning of the nodes of the network into disjoint dominating sets. These sets represent a series of virtual backbones for wireless sensor networks to be activated successively, resulting in more balanced energy consumption and increased network robustness. In this study, we address the domatic partition problem in random geometric graphs by investigating several vertex coloring algorithms both topology and geometry-aware, color-adaptive and randomized. Graph coloring produces color classes with each class representing an independent set of vertices. The disjoint maximal independent sets constitute a collection of disjoint dominating sets that offer good network coverage. Furthermore, if we relax the full domination constraint then we obtain a partitioning of the network into disjoint dominating and nearly-dominating sets of nearly equal size, providing better redundancy and a near-perfect node coverage yield. In addition, these independent sets can be the basis for clustering a very large sensor network with minimal overlap between the clusters leading to increased efficiency in routing, wireless transmission scheduling and data-aggregation. We also observe that in dense random deployments, certain coloring algorithms yield a packing of the nodes into independent sets each of which is relatively close to the perfect placement in the triangular lattice.