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Research Projects
Reeb Graph Computation for a PL Function on a Simplicial Complex
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Abstract
Reeb graph of a real-valued function on a topological space, is a compact representation of the domain of the function. It is achieved by contracting connected components of any preimage of a real number into points. Reeb graph generalizes the more familiar contour tree. In this project, we considered computation of the Reeb graph for a PL function for any dimension. We give a new algorithm that achieves the best running times. Reeb graph can be considered a basic tool in Computational Topology and has found many applications. For example, the 0'th persistence diagram of the level set filteration of the function can be read from the Reeb graph.
Advisor(s): Herbert Edelsbrunner
Pankaj Agarwal, Paul Bendich