Employing (1 − ∊) Dominating Set Partitions as Backbones in Wireless Sensor Networks

Abstract

For a random geometric graph G(n, r) of minimum degree δ, we introduce an efficient algorithm for selecting (δ + 1) backbones with disjoint node sets that are each independent (1 − ε) dominating sets of G. The backbone node sets are determined by a graph coloring algorithm employing only the topology (not the geometry) of G(n, r), and the backbone links are selected with link lengths in a narrow window between r and 2r and further to form a planar graph backbone. For large vertex sets (n = 1600, 3200) the resulting backbones are shown to each cover typically over 99% of the vertices of G (i.e. ε < 0.01), with about 30% being fully dominating, which is consistent with the 1 4 constant approximation factor algorithm proposed recently in [23] for the domatic partition problem in Unit Disk Graphs. We establish experimentally by measures of node degrees, link lengths, and interior triangular face counts that each individual backbone has most of the coverage behavior and routing convenience of the triangular "perfect packing" lattice. We further show for each sample G(n, r) that the relatively few vertices not covered by all (δ + 1) backbones are covered by most of the backbones. Hence backbone rotation in a wireless sensor network would reach all sensors (vertices) sufficiently frequently. Our novel backbone generation algorithm confirms experimentally the existence of these (δ + 1) backbones in a random geometric graph, and provides an efficient topologically based centralized algorithm for determining the backbones. We also point out that our novel backbone construction method is flexible such that any efficient coloring algorithm can be plugged into it. In this paper, we experiment with several coloring algorithms: Smallest Last, Largest First, Lexicographic, Radial Sweep and Random and we compare their respective performance. Our emphasis is, however, on SL since it offers robust properties and interesting expected behavior. We also experiment with several random node distributions: uniform, skewed and normal in both unit square and disk of which we also discuss the results. * Boby B. Lyle School of Engineering. Southern Methodist University. Dallas, TX 75275-0122, USA.

Randomized and Optimal Algorithms for k-Lifetime Dominating Set in Wireless Sensor Networks

“…Based on the graph coloring method, Mahjoub and Matula solved the domatic partition problem in random geometric graph and provided up to ( + 1) disjoint (1 − ε) dominating sets on a large range of experimental graphs [4]. They carried out further research by proposing a more practical solution to the distributed ( +1) domatic partition problem based on the localized graph coloring method [5].…”

Connected Domatic Packings in Node-capacitated Graphs

“…Connected domatic partitions and packings have several applications in the design of wireless networks. In these applications, a connected dominating set is used as a virtual backbone, and the rest of the nodes use the connected dominating set to exchange messages and route traffic [6,7,21]. Motivated by the goal of improving the energy efficiency and the lifetime of the network, several papers [22][23][24] have proposed using several connected dominating sets; these approaches first compute a large connected domatic packing or partition and they rotate between the connected dominating sets.…”