  Iterated localization is considered where each node of a network needs to get
localized (find its location on 2-D plane), when initially only a subset of
nodes have their location information. The iterated localization process
proceeds as follows. Starting with a subset of nodes that have their location
information, possibly using global positioning system (GPS) devices, any other
node gets localized if it has three or more localized nodes in its radio range.
The newly localized nodes are included in the subset of nodes that have their
location information for the next iteration. This process is allowed to
continue, until no new node can be localized. The problem is to find the
minimum size of the initially localized subset to start with so that the whole
network is localized with high probability. There are intimate connections
between iterated localization and bootstrap percolation, that is well studied
in statistical physics. Using results known in bootstrap percolation, we find a
sufficient condition on the size of the initially localized subset that
guarantees the localization of all nodes in the network with high probability.
