Harish Doraiswamy, Aneesh Sood, and Vijay Natarajan. SoCG 2010: ACM Symposium on Computational Geometry, Video / Multimedia track, 2010.

Abstract

The Reeb graph of a scalar function represents the evolution of the
topology of its level sets. In this video, we describe a near-optimal
output-sensitive algorithm for computing the Reeb graph of scalar
functions defined over manifolds. Key to the simplicity and efficiency
of the algorithm is an alternate definition of the Reeb graph
that considers equivalence classes of level sets instead of individual
level sets. The algorithm works in two steps. The first step locates
all critical points of the function in the domain. Arcs in the Reeb
graph are computed in the second step using a simple search procedure
that works on a small subset of the domain that corresponds
to a pair of critical points. The algorithm is also able to handle
non-manifold domains.

Constructing Reeb Graphs using Cylinder Maps - A video illustration (Download)
This video illustrates the two-step algorithm for computing the Reeb graph of a piecewise-linear (PL) function using Cylinder maps.