Wireless networks and random geometric graphs

In this paper, mobile ad-hoc networks are studied. Chen and Jia (2001) proposed a routing algorithm by utilizing multiple communication channels and localizing the routing information (routing tables) for mobile stations within the wireless network. The routing algorithm relies on a spanning tree of the underlying network. It is proven that both the construction of the spanning tree and the routing algorithm are efficient. The routing algorithm is also reliable because of the frequent update of the spanning tree which the routing scheme is based on. The underlying network is a random geometric graph G(A,n) formed on a set of uniformly randomly located points in the unit disk, in which two vertices are adjacent if and only if their Euclidean distance is at most A.