The Tree Containment problem consists in deciding whether a phylogenetic tree is displayed by a phylogenetic network. It is NP-hard in general, although polynomial-time algorithms were found for restricted cases when constraints are given on thestructure of the phylogenetic network. Considering this problem as a special case of directed subgraph homeomorphism allows us to design several new algorithmic approaches to address it efficiently in practice, using the pebble game algorithm introduced to solve this problem. After proposing a SAT formulation of the problem, we turn to database theory, by first showing how to design a Datalog program to solve the problem. We then show how to optimize this approach to solve the problem faster in practice.