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Computing Homology: A Global Reduction Approach

  • David Corriveau
  • Madjid Allili
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

A new algorithm to compute the homology of a finitely generated chain complex is proposed in this work. It is based on grouping algebraic reductions of the complex into structures that can be encoded as directed acyclic graphs. This leads to sequences of projection maps that reduce the number of generators in the complex while preserving its homology. This organization of reduction pairs allows to update 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, this method gives the homology generators for a small additional cost.

Keywords

Homology Computation Reduction Directed Acyclic Graphs Generators 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • David Corriveau
    • 1
  • Madjid Allili
    • 2
  1. 1.Dept. of Computer ScienceUniversité de SherbrookeSherbrookeCanada
  2. 2.Dept. of Computer ScienceBishop’s UniversitySherbrookeCanada

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