Address autoconfiguration is an important mechanism required to set the IP
address of a node automatically in a wireless network. The address
autoconfiguration, also known as initialization or naming, consists to give a
unique identifier ranging from 1 to n for a set of n indistinguishable
nodes. We consider a wireless network where n nodes (processors) are randomly
thrown in a square X, uniformly and independently. We assume that the network
is synchronous and two nodes are able to communicate if they are within
distance at most of r of each other (r is the transmitting/receiving
range). The model of this paper concerns nodes without the collision detection
ability: if two or more neighbors of a processor u transmit concurrently at
the same time, then u would not receive either messages. We suppose also that
nodes know neither the topology of the network nor the number of nodes in the
network. Moreover, they start indistinguishable, anonymous and unnamed. Under
this extremal scenario, we design and analyze a fully distributed protocol to
achieve the initialization task for a wireless multihop network of n nodes
uniformly scattered in a square X. We show how the transmitting range of the
deployed stations can affect the typical characteristics such as the degrees
and the diameter of the network. By allowing the nodes to transmit at a range
r= \sqrt{\frac{(1+\ell) \ln{n} \SIZE}{\pi n}} (slightly greater than the one
required to have a connected network), we show how to design a randomized
protocol running in expected time O(n3/2log2n) in order to assign a
unique number ranging from 1 to n to each of the n participating nodes