After the proposed event is executed, the related occupations, correlations, and hopping frequencies are updated. Since a given site may be involved in multiple migration events, all events with sites associated with the proposed event are updated. The number of events that require updation after a proposed event is defined as the coupling strength of events, which can influence the computational performance of kMC (see Sec. IV). We use a pre-computed table (event_kernel) to quickly identify all events that need to be updated.