  Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS
problem asks to compute a minimum number of vertices to be marked as trackers,
such that the sequence of trackers encountered in each s-t path is unique.
TRACKING PATHS is NP-hard in both directed and undirected graphs in general. In
this paper we give a collection of polynomial time algorithms for some
restricted versions of TRACKING PATHS. We prove that TRACKING PATHS is
polynomial time solvable for chordal graphs and tournament graphs. We prove
that TRACKING PATHS is NP-hard in graphs with bounded maximum degree
$\delta\geq 6$, and give a $2(\delta+1)$-approximate algorithm for the same. We
also analyze the version of tracking s-t paths where paths are tracked using
edges instead of vertices, and we give a polynomial time algorithm for the
same. Finally, we show how to reconstruct an s-t path, given a sequence of
trackers and a tracking set for the graph in consideration.
