Data structures and network algorithms
Data structures and network algorithms
An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
A computationally intractable problem on simplicial complexes
Computational Geometry: Theory and Applications
Handbook of discrete and computational geometry
On discrete Morse functions and combinatorial decompositions
Discrete Mathematics
Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Edgebreaker: a simple compression for surfaces with handles
Proceedings of the seventh ACM symposium on Solid modeling and applications
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Applications of Forman's Discrete Morse Theory to Topology Visualization and Mesh Compression
IEEE Transactions on Visualization and Computer Graphics
Zigzag persistent homology in matrix multiplication time
Proceedings of the twenty-seventh annual symposium on Computational geometry
A fast algorithm to compute cohomology group generators of orientable 2-manifolds
Pattern Recognition Letters
Perfect discrete Morse functions on 2-complexes
Pattern Recognition Letters
Extraction of Dominant Extremal Structures in Volumetric Data Using Separatrix Persistence
Computer Graphics Forum
Extraction of feature lines on surface meshes based on discrete morse theory
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Parameterized complexity of discrete morse theory
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Morse function has been defined on a manifold, then information about its topology can be deduced from its critical elements. The main objective of this paper is to introduce a linear algorithm to define optimal discrete Morse functions on discrete 2-manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality.