Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest. In this work we consider the wide-spread compartment model where each node is in one of several states (or compartments). Nodes change their state randomly after an exponentially distributed waiting time and according to a given set of rules. For networks of realistic size, even the generation of only a single stochastic trajectory of a spreading process is computationally very expensive.

Here, we propose a novel simulation approach, which combines the advantages of event-based simulation and rejection sampling. Our method outperforms state-of-the-art methods in terms of absolute runtime and scales significantly better while being statistically equivalent.