Pseudonymization is a promising technique for publishing a trajectory location data set in a privacy-preserving way. However, it is not trivial to determine whether a given data set is safely publishable against an adversary with partial knowledge about users’ movements. We therefore formulate this safety decision problem based on the framework of constraint satisfaction problems (CSPs) and evaluate its performance with a real location data set. We show that our approach with an existing CSP solver outperforms a polynomial-time verification algorithm, which is designed particularly for this safety problem.