## 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.