  Consider the following routing problem in the context of a large scale
network $G$, with particular interest paid to power law networks, although our
results do not assume a particular degree distribution. A small number of nodes
want to exchange messages and are looking for short paths on $G$. These nodes
do not have access to the topology of $G$ but are allowed to crawl the network
within a limited budget. Only crawlers whose sample paths cross are allowed to
exchange topological information. In this work we study the use of random walks
(RWs) to crawl $G$. We show that the ability of RWs to find short paths bears
no relation to the paths that they take. Instead, it relies on two properties
of RWs on power law networks: 1) RW's ability observe a sizable fraction of the
network edges; and 2) an almost certainty that two distinct RW sample paths
cross after a small percentage of the nodes have been visited. We show
promising simulation results on several real world networks.
