  We show that it is possible to use a quantum walk to find a path from one
marked vertex to another. In the specific case of $M$ stars connected in a
chain, one can find the path from the first star to the last one in
$O(M\sqrt{N})$ steps, where $N$ is the number of spokes of each star. First we
provide an analytical result showing that by starting in a phase-modulated
highly superposed initial state we can find the path in $O(M\sqrt{N}\log M)$
steps. Next, we improve this efficiency by showing that the recovery of the
path can also be performed by a series of successive searches when we start at
the last known position and search for the next connection in $O(\sqrt{N})$
steps leading to the overall efficiency of $O(M\sqrt{N})$. For this result we
use the analytical solution that can be obtained for a ring of stars of double
the length of the chain.
