Smaller Connected Dominating Sets in Ad Hoc and Sensor Networks based on Coverage by Two-Hop Neighbors

In this paper, we focus on the construction of an efficient dominating set in ad hoc and sensor networks. A set of nodes is said to be dominating if each node is either itself dominant or neighbor of a dominant node. Application of such a set may for example be broadcasting, where the size of the set greatly impacts on energy consumption. Obtaining small sets is thus of prime importance. As a basis for our work, we use a heuristic given by Dai and Wu for constructing such a set. Their approach, in conjunction with the elimination of message overhead by Stojmenović, has been recently shown to be an excellent compromise with respect to a wide range of metrics. In this paper, we present an enhanced definition to obtain smaller sets in the specific case where 2-hop information is considered. In our new definition, a node 𝓊 is not dominant if there exists in its 2-hop neighborhood a connected set of nodes with higher priorities that covers μ and its 1-hop neighbors. This new rule requires the same level of knowledge used by the original heuristic: only neighbors of nodes and neighbors of neighbors must be known to apply it. However, it takes advantage of some topological knowledge originally not taken into account, that may be used to deduce communication links between 1 -hop and 2-hop neighbors. We provide the proof that the new set is a subset of the one obtained with the original heuristic. We also give the proof that our set is always dominating for any graph, and connected for any connected graph. Two versions are considered: with topological and positional information, which differ in whether or not nodes are aware of links between their 2-hop neighbors that are not 1-hop neighbors. An algorithm for locally applying the concept at each node is described. We finally provide experimental data that demonstrates the superiority of our rule in obtaining smaller dominating sets. A centralized algorithm is used as a benchmark in the comparisons. The overhead of the size of connected dominating set is reduced by about 15% with the topological variant and by about 30% with the positional variant of our new definition.