Algorithms

The algorithms used in RedHom are based on the following papers:

• S. Harker, K. Mischaikow, M. Mrozek, V. Nanda, H. Wagner, M. Juda, P. Dłotko
  The Efficiency of a Homology Algorithm based on Discrete Morse Theory and Coreductions,
  published version in: Proceedings of the 3rd International Workshop on Computational Topology in Image Context, Chipiona, Spain, November 2010 (Rocio Gonzalez Diaz Pedro Real Jurado (Eds.)), Image A Vol. 1(2010), 41-47.
• P. Dłotko, T. Kaczynski, M. Mrozek, Th. Wanner,
  Coreduction Homology Algorithm for Regular CW-Complexes,
  Discrete and Computational Geometry, accepted.
• M. Mrozek, Th. Wanner
  Coreduction homology algorithm for inclusions and persistent homology,
  Computers and Mathematics with Applications, accepted.
• M. Juda, M. Mrozek,
  $Z_2$-Homology of 2-manifolds may be computed in $O(n\log^{*}(n))$ time,
  preprint.
• M. Mrozek, B. Batko
  Homology of representable sets,
  published version in: Annales Polonici Mathematici 97.3(2010), 243-252.
• M. Mrozek, B. Batko,
  Coreduction Homology Algorithm
  published version in: Discrete and Computational Geometry, 41(2009), 96-118.
• M. Mrozek, P. Pilarczyk, N. Żelazna,
  Homology Algorithm Based on Acyclic Subspace
  published version in: Computers and Mathematics with Applications, 55(2008), 2395–2412.
• K. Mischaikow, M. Mrozek, P. Pilarczyk,
  Graph Approach to the Computation of the Homology of Continuous Maps,
  published version in: Foundations of Computational Mathematics, 5(2005), 199-229
• T. Kaczynski M. Mrozek and M. Slusarek,
  Homology Computation by Reduction of Chain Complexes,
  published version in: Computers and Mathematics with Applications, 35(1998), no. 4, 59--70.