Loops in Reeb graphs of 2-manifolds
Publication
, Journal Article
Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V
Published in: Discrete and Computational Geometry
January 1, 2004
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
Discrete and Computational Geometry
DOI
ISSN
0179-5376
Publication Date
January 1, 2004
Volume
32
Issue
2
Start / End Page
231 / 244
Related Subject Headings
- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., & Pascucci, V. (2004). Loops in Reeb graphs of 2-manifolds. Discrete and Computational Geometry, 32(2), 231–244. https://doi.org/10.1007/s00454-004-1122-6
Cole-McLaughlin, K., H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. “Loops in Reeb graphs of 2-manifolds.” Discrete and Computational Geometry 32, no. 2 (January 1, 2004): 231–44. https://doi.org/10.1007/s00454-004-1122-6.
Cole-McLaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Discrete and Computational Geometry. 2004 Jan 1;32(2):231–44.
Cole-McLaughlin, K., et al. “Loops in Reeb graphs of 2-manifolds.” Discrete and Computational Geometry, vol. 32, no. 2, Jan. 2004, pp. 231–44. Scopus, doi:10.1007/s00454-004-1122-6.
Cole-McLaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Discrete and Computational Geometry. 2004 Jan 1;32(2):231–244.
Published In
Discrete and Computational Geometry
DOI
ISSN
0179-5376
Publication Date
January 1, 2004
Volume
32
Issue
2
Start / End Page
231 / 244
Related Subject Headings
- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics