A variant of connected dominating set in unit disk graphs for applications in communication networks

This paper considers a variant of the connected dominating set (CDS) problem in a unit disk graph G = (V, E). The considered problem consists in minimizing the number of CDS vertices that belong to a subset V' ⊆V. As far as we know, this problem has not been treated in the literature. Nevertheless, its resolution would be useful in many communication network applications, such as the selection of relay nodes in heterogenous wireless ad hoc networks where only a subset of powerful nodes (e.g., energy or memory rich nodes) may form the network backbone act as relays, or where it is preferable to select relays from these nodes and minimize the number of non-powerful nodes that act as relays. Replacement of non-powerful nodes might be necessary either at the initialization (after deployment), or during the network lifetime, which justifies the need to minimize their number. The problem is first modeled and reduced to the minimum weighted connected dominating set (WCDS) problem in a vertex weighted graph, and then it is resolved by taking advantage of the simple form of the weight function using integer linear programming (ILP). A heuristic is also proposed for large scale resolution. Simulation results confirms closeness of the proposed heuristic to the optimal solution obtained by the ILP, and scalability of the heuristic.