Embedding phylogenetic trees in networks of low treewidth

Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called $\text{textsc}TreeContainment$, arises when validating networks constructed by phylogenetic inference methods.We present the first algorithm for (rooted) $\text{textsc}TreeContainment$ using the treewidth $t$ of the input network $N$ as parameter, showing that the problem can be solved in $2^{O(t^2)}\cdot \mathrm{\mid }N\mathrm{\mid }$ time and space.