Experience shows that in systems where process executions are not strictly enforced by process models, often deviations occur. Alignments between logged process executions and models reveal useful insights and can be used for both conformance checking and performance analysis. In this article, we present a memory-e¿cient approach using marking equations of Petri nets to calculate optimal alignments between process executions and process models. A comparative study shows that in most cases the approach signi¿cantly reduces the memory required. This makes it possible to analyze larger logs and models using alignments. The more deviations exist, the better the approach performs compared to the approaches without using marking equations. The ap...