on the fundamental limits of topology control
We consider the effect of link dynamics on topology control in large ad hoc and sensor networks. By link dynamics we mean the length ratio of the longest and shortest link adjacent to the same node. We show a new fundamental limit of topology control: if the number of nodes grow to infinity, while link dynamics remains bounded, then no topology control algorithm can keep a large network connected with high probability. Moreover, bounded link dynamics prevents connectivity in the limit without any assumption on the node degrees or transmission ranges. Our results hold in a model that is much more general than the frequently used assumption of uniformly distributed nodes in a regularly shaped planar domain. Since link dynamics is expected to be bounded in practice, the results strenghten the theoretical basis for the argument that a large ad hoc or sensor network is unable to maintain connectivity if it has a flat, random organization without additional structure.
topology control connectivity fundamental performance limits ad hoc network