Decentralised topology control algorithms for connectivity of distributed Wireless Sensor networks

In this paper, we study the problem of maintaining the connectivity of a Wireless Sensor Network (WSN) using decentralised topology control protocols. Previous algorithms on topology control require the knowledge of the density of nodes (λ) in the sensing region. However, if λ varies continuously over time, updating this information, at all nodes is impractical. Therefore, in addition to efficient maintenance of connectivity, we also wish to reduce the control overhead of the topology control algorithm. In the absence of information regarding λ we study the connectivity properties of WSNs by means of giant components. We show that by maintaining the out-degree at each node as five will give rise to a giant connected component in the network. We also show that this is the smallest value that can maintain a giant connected component irrespective of how often or by how much λ changes.