Wireless networks in home, office and sensor applications consist of
nodes with low mobility. Most of these networks have at least a few powerful
machines additionally connected by a wireline network. Topology informa-
tion of the wireless network at these powerful nodes can be used to control
transmission power, avoid congestion, compute routing tables, discover re-
sources, and to gather data. In this paper we propose an algorithm for topol-
ogy discovery in wireless networks with slow moving nodes and present var-
ious performance characteristics of this algorithm. The proposed algorithm
discovers all links and nodes in a stable wireless network and has an excellent
message complexity: the algorithm has an optimal message complexity in a
stable network and the overhead degrades slowly with increasing mobility of
the nodes.