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We present a comparison of the kinetic Activation-Relaxation Technique(k-ART) and the Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC), twooff-lattice, on-the-fly kinetic Monte Carlo (KMC) techniques that were recentlyused to solve several materials science problems. We show that if the initialdisplacements are localized the dimer method and the Activation-RelaxationTechnique \emph{nouveau} provide similar performance. We also show that k-ARTand SEAKMC, although based on different approximations, are in agreement witheach other, as demonstrated by the examples of 50 vacancies in a 1950-atom Febox and of interstitial loops in 16000-atom boxes. Generally speaking, k-ART'streatment of geometry and flickers is more flexible, e.g. it can handleamorphous systems, and rigorous than SEAKMC's, while the later's concept ofactive volumes permits a significant speedup of simulations for the systemsunder consideration and therefore allows investigations of processes requiringlarge systems that are not accessible if not localizing calculations.

Kinetic Activation-Relaxation Technique and Self-Evolving Atomistic Kinetic Monte Carlo: Comparison of on-the-fly kinetic Monte Carlo algorithms