This algorithm maximally leverages the efficient algorithms available to compute the loop-free version of the Reeb graph. It partitions the input into subsets whose Reeb graph do not contain any loops and merges the loop-free graphs in linear time to construct the Reeb graph of the input. The algorithm has a worst case running time of

Reeb graph of the height function defined on a few objects. Reeb graph tracks the topology of level sets.

- Harish Doraiswamy

- Harish Doraiswamy and Vijay Natarajan.

Computing Reeb graphs as a union of contour trees.*IEEE Transactions on Visualization and Computer Graphics*, 19 (2), 2013, 249-262.