On Improving Connectivity of Static Ad-Hoc Networks by Adding Nodes

Abstract — The connectivity of a given static, disconnected adhoc network can be improved by placing additional nodes in the network, forming connections between separate clusters of connected nodes. Finding optimal locations to place the additional nodes is a difficult problem. We give definitions of two problems: connecting the network with a minimal number of additional nodes, and maximizing utility from a given number of additional nodes in case complete connectivity cannot be established. The former problem reduces in a limit case to that of the Euclidean Steiner minimal tree. We present heuristic algorithms that can be used to efficiently attack these problems: a minimum spanning tree algorithm and two greedy algorithms, all applicable to both problems. The algorithms are feasible in their computation effort. We study the performance of these algorithms by simulations. We also consider the generalization of the problem to k-connectivity and recognize its relation to another NP-hard problem, namely, that of graph augmentation. I