Research Projects

Reeb Graph Computation for a PL Function on a Simplicial Complex

Speaker:Salman Parsa
salparsa at cs.duke.edu
Date: Tuesday, June 12, 2012
Time: 2:00pm - 3:30pm
Location: D344 LSRC, Duke
Pankaj Agarwal, Paul Bendich

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