  We investigate the applicability of the synchronous relaxation (SR) algorithm
to parallel kinetic Monte Carlo simulations of simple models of thin-film
growth. A variety of techniques for optimizing the parallel efficiency are also
presented. We find that the parallel efficiency is determined by three main
factors $-$ the calculation overhead due to relaxation iterations to correct
boundary events in neighboring processors, the (extreme) fluctuations in the
number of events per cycle in each processor, and the overhead due to
interprocessor communications. Due to the existence of fluctuations and the
requirement of global synchronization, the SR algorithm does not scale, i.e.
the parallel efficiency decreases logarithmically as the number of processors
increases. The dependence of the parallel efficiency on simulation parameters
such as the processor size, domain decomposition geometry, and the ratio $D/F$
of the monomer hopping rate $D$ to the deposition rate $F$ is also discussed.
