Building (1-ε) dominating sets partition as backbones in wireless sensor networks using distributed graph coloring

Abstract

We recently proposed in [19,20] to use sequential graph coloring as a systematic algorithmic method to build (1-ε) dominating sets partition in Wireless Sensor Networks (WSN) modeled as Random Geometric Graphs (RGG). The resulting partition of the network into dominating and almost dominating sets can be used as a series of rotating backbones in a WSN to prolong the network lifetime for the benefit of various applications. Graph coloring algorithms in RGGs offer proven constant approximation guarantees on the chromatic number. In this paper, we demonstrate that by combining a local vertex ordering with the greedy color selection strategy, we can in practice, minimize the number of colors used to color an RGG within a very narrow window of the chromatic number and concurrently also obtain a domatic partition size within a competitive factor of the domatic number. We also show that the minimal number of colors results in the first (δ+1) color classes being provably dense enough to form independent sets that are (1-ε) dominating. The resulting first (δ+1) independent sets, where δ is the minimum degree of the graph, are shown to cover typically over 99% of the nodes (e.g. ε<0.01), with at least 20% being fully dominating. These independent sets are subsequently made connected through virtual links using localized proximity rules to constitute planar connected backbones. The novelty of this paper is that we extend our recent work in [20] into the distributed setting and present an extensive experimental evaluation of known distributed coloring algorithms to answer the (1-ε) dominating sets partition problem. These algorithms are both topology and geometry-based and yield O(1) times the chromatic number. They are also shown to be inherently localized with running times in O(Δ) where Δ is the maximum degree of the graph. © 2010 Springer-Verlag.