The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology

  • Jean-Daniel Boissonnat
  • Tamal K. Dey
  • Clément Maria
Conference paper

DOI: 10.1007/978-3-642-40450-4_59

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)
Cite this paper as:
Boissonnat JD., Dey T.K., Maria C. (2013) The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology. In: Bodlaender H.L., Italiano G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean-Daniel Boissonnat
    • 1
  • Tamal K. Dey
    • 2
  • Clément Maria
    • 1
  1. 1.INRIA Sophia Antipolis-MéditerranéeFrance
  2. 2.The Ohio State UniversityUSA

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