In the context of high-dimensional and massive datasets in Bayesian inference, it has become crucial to develop Markov-chain Monte Carlo sampling methods which present better scaling properties in terms of dynamics, but also in terms of computational complexity: Could it be possible to derive an exact method which only needs to compute a small number of terms per move? This presentation will present the Clock Monte Carlo method and how it uses the factorization of the acceptance probabilities to produce moves in a constant O(1) complexity. This method is inspired from the factorization trick and thinning method originally used in MCMC sampling based on piecewise deterministic Markov processes. The factorization trick can lead to an important dynamical slow down, for instance in case of strong frustration in physical systems, and mitigating solutions will be discussed.