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Erschienen in:
2013 | OriginalPaper | Buchkapitel
The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology
verfasst von : Jean-Daniel Boissonnat, Tamal K. Dey, Clément Maria
Erschienen in: Algorithms – ESA 2013
Verlag: Springer Berlin Heidelberg
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Persistent homology with coefficients in a field
$\mathbb{F}$
coincides with the same for cohomology because of duality. We propose an implementation of a recently introduced algorithm for persistent cohomology that attaches annotation vectors with the simplices. We separate the representation of the simplicial complex from the representation of the cohomology groups, and introduce a new data structure for maintaining the annotation matrix, which is more compact and reduces substancially the amount of matrix operations. In addition, we propose a heuristic to simplify further the representation of the cohomology groups and improve both time and space complexities. The paper provides a theoretical analysis, as well as a detailed experimental study of our implementation and comparison with state-of-the-art software for persistent homology and cohomology.