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Corriveau, D. and Allili, M. (2009) Computing Homology: A Global Reduction Approach. In: Brlek, S., Reutenauer, C. and Provençal, X., Eds., Discrete Geometry for Computer Imagery: Proceedings of 15th IAPR International Conference, DGCI 2009, Springer, Berlin Heidelberg, 313-324.
http://dx.doi.org/10.1007/978-3-642-04397-0_27

has been cited by the following article:

• TITLE: A Global Reduction Based Algorithm for Computing Homology of Chain Complexes

  AUTHORS: Madjid Allili, David Corriveau

  KEYWORDS: Homology Algorithm, Chain Complex, Homology Generators

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.3, February 26, 2016

  ABSTRACT: In this paper, we propose a new algorithm to compute the homology of a finitely generated chain complex. Our method is based on grouping several reductions into structures that can be encoded as directed acyclic graphs. The organized reduction pairs lead to sequences of projection maps that reduce the number of generators while preserving the homology groups of the original chain complex. This sequencing of reduction pairs allows updating the boundary information in a single step for a whole set of reductions, which shows impressive gains in computational performance compared to existing methods. In addition, our method gives the homology generators for a small additional cost.