  We study the Short Path Packing problem which asks, given a graph $G$,
integers $k$ and $\ell$, and vertices $s$ and $t$, whether there exist $k$
pairwise internally vertex-disjoint $s$-$t$ paths of length at most $\ell$. The
problem has been proven to be NP-hard and fixed-parameter tractable
parameterized by $k$ and $\ell$. Most previous research on this problem has
been theoretical with limited practical implemetations. We present an exact
FPT-algorithm based on a search-tree approach in combination with greedy
localization. While its worst case runtime complexity of $(k\cdot
\ell^2)^{k\cdot \ell}\cdot n^{O(1)}$ is larger than the state of the art, the
nature of search-tree algorithms allows for a broad range of potential
optimizations. We exploit this potential by presenting techniques for input
preprocessing, early detection of trivial and infeasible instances, and
strategic selection of promising subproblems. Those approaches were implemented
and heavily tested on a large dataset of diverse graphs. The results show that
our heuristic improvements are very effective and that for the majority of
instances, we can achieve fast runtimes.
