  Comparing observed behavior (event data generated during process executions)
with modeled behavior (process models), is an essential step in process mining
analyses. Alignments are the de-facto standard technique for calculating
conformance checking statistics. However, the calculation of alignments is
computationally complex since a shortest path problem must be solved on a state
space which grows non-linearly with the size of the model and the observed
behavior, leading to the well-known state space explosion problem. In this
paper, we present a novel framework to approximate alignments on process trees
by exploiting their hierarchical structure. Process trees are an important
process model formalism used by state-of-the-art process mining techniques such
as the inductive mining approaches. Our approach exploits structural properties
of a given process tree and splits the alignment computation problem into
smaller sub-problems. Finally, sub-results are composed to obtain an alignment.
Our experiments show that our approach provides a good balance between accuracy
and computation time.
