  Building on previous Bayesian approaches, we introduce a novel formulation of
probabilistic cross-identification, where detections are directly associated to
(hypothesized) astronomical objects in a globally optimal way. We show that
this new method scales better for processing multiple catalogs than enumerating
all possible candidates, especially in the limit of crowded fields, which is
the most challenging observational regime for new-generation astronomy
experiments such as the Rubin Observatory Legacy Survey of Space and Time
(LSST). Here we study simulated catalogs where the ground-truth is known and
report on the statistical and computational performance of the method. The
paper is accompanied by a public software tool to perform globally optimal
catalog matching based on directional data.
