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Loops in Reeb graphs of 2-manifolds

Publication ,  Journal Article
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
Published in: Proceedings of the Annual Symposium on Computational Geometry
January 1, 2003

Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

Duke Scholars

Published In

Proceedings of the Annual Symposium on Computational Geometry

DOI

Publication Date

January 1, 2003

Start / End Page

344 / 350
 

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Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., & Pascucci, V. (2003). Loops in Reeb graphs of 2-manifolds. Proceedings of the Annual Symposium on Computational Geometry, 344–350. https://doi.org/10.1145/777842.777844
Cole-McLaughlin, K., H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. “Loops in Reeb graphs of 2-manifolds.” Proceedings of the Annual Symposium on Computational Geometry, January 1, 2003, 344–50. https://doi.org/10.1145/777842.777844.
Cole-McLaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Proceedings of the Annual Symposium on Computational Geometry. 2003 Jan 1;344–50.
Cole-McLaughlin, K., et al. “Loops in Reeb graphs of 2-manifolds.” Proceedings of the Annual Symposium on Computational Geometry, Jan. 2003, pp. 344–50. Scopus, doi:10.1145/777842.777844.
Cole-McLaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Proceedings of the Annual Symposium on Computational Geometry. 2003 Jan 1;344–350.

Published In

Proceedings of the Annual Symposium on Computational Geometry

DOI

Publication Date

January 1, 2003

Start / End Page

344 / 350