Approximating the geographical area of a wireless ad-hoc network

Wireless ad-hoc networks are typically deployed in a decentralized way, without an authority that determines the location of nodes or the time they join the network. Additionally, existing nodes may fail during network lifetime. Consequently, the geographical span (area) of the network is irregular and unknown. However, if known, this information can be used to improve efficiency of many wireless applications; in some existing applications this information is necessary for their operation in the real use cases. For this purpose, we propose a distributed algorithm that determines the geographical network area. It is the first algorithm that simultaneously discovers network border, approximates the network area with a data structure of a constant size, and disseminates this information to all network nodes. Our algorithm uses only the nodes´ local information, has a constant computational complexity and is resilient to link unreliability. The algorithm is evaluated by simulation on realistic network topologies of different sizes. The simulations demonstrate that the algorithm has high accuracy in its estimation of the network area, scales well with the number of nodes, and that it creates a low communication overhead.