Given two datasets A and B, their exclusive closest pairs (ECP) join is a one-to-one assignment of objects from the two datasets, such that (i) the closest pair (a, b) in A×B is in the result and (ii) the remaining pairs are determined by removing objects a, b from A, B respectively, and recursively searching for the next closest pair. An application of exclusive closest pairs is the computation of (car, parking slot) assignments. In this paper, we propose algorithms for the computation and continuous monitoring of ECP joins in memory, given a stream of events that indicate dynamic assignment requests and releases of pairs. Experimental results on a system prototype demonstrate the efficiency of our solutions in practice.