  Given an undirected graph, $G$, and vertices, $s$ and $t$ in $G$, the
tracking paths problem is that of finding the smallest subset of vertices in
$G$ whose intersection with any $s$-$t$ path results in a unique sequence. This
problem is known to be NP-complete and has applications to animal migration
tracking and detecting marathon course-cutting, but its approximability is
largely unknown. In this paper, we address this latter issue, giving novel
algorithms having approximation ratios of $(1+\epsilon)$, $O(\lg OPT)$ and
$O(\lg n)$, for $H$-minor-free, general, and weighted graphs, respectively. We
also give a linear kernel for $H$-minor-free graphs and make improvements to
the quadratic kernel for general graphs.
