  Given an undirected graph $G=(V,E)$, vertices $s,t\in V$, and an integer $k$,
Tracking Shortest Paths requires deciding whether there exists a set of $k$
vertices $T\subseteq V$ such that for any two distinct shortest paths between
$s$ and $t$, say $P_1$ and $P_2$, we have $T\cap V(P_1)\neq T\cap V(P_2)$. In
this paper, we give the first polynomial size kernel for the problem.
Specifically we show the existence of a kernel with $\mathcal{O}(k^2)$ vertices
and edges in general graphs and a kernel with $\mathcal{O}(k)$ vertices and
edges in planar graphs for the Tracking Paths in DAG problem. This problem
admits a polynomial parameter transformation to Tracking Shortest Paths, and
this implies a kernel with $\mathcal{O}(k^4)$ vertices and edges for Tracking
Shortest Paths in general graphs and a kernel with $\mathcal{O}(k^2)$ vertices
and edges in planar graphs. Based on the above we also give a single
exponential algorithm for Tracking Shortest Paths in planar graphs.
