  With the popularization of Topological Data Analysis, the Reeb graph has
found new applications as a summarization technique in the analysis and
visualization of large and complex data, whose usefulness extends beyond just
the graph itself. Pairing critical points enables forming topological
fingerprints, known as persistence diagrams, that provides insights into the
structure and noise in data. Although the body of work addressing the efficient
calculation of Reeb graphs is large, the literature on pairing is limited. In
this paper, we discuss two algorithmic approaches for pairing critical points
in Reeb graphs, first a multipass approach, followed by a new single-pass
algorithm, called Propagate and Pair.
