Coreduction Homology Algorithm for Regular CW-Complexes |
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Authors: | Paweł Dłotko Tomasz Kaczynski Marian Mrozek Thomas Wanner |
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Institution: | 1.Institute of Computer Science,Jagiellonian University,Kraków,Poland;2.Département de Mathématiques,Université de Sherbrooke,Sherbrooke,Canada;3.Division of Computational Mathematics,WSB-NLU,Nowy Sa?cz,Poland;4.Department of Mathematical Sciences,George Mason University,Fairfax,USA |
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Abstract: | In this paper we present a new algorithm for computing the homology of regular CW-complexes. This algorithm is based on the
coreduction algorithm due to Mrozek and Batko and consists essentially of a geometric preprocessing algorithm for the standard
chain complex generated by a CW-complex. By employing the concept of S-complexes the original chain complex can—in all known
practical cases—be reduced to a significantly smaller S-complex with isomorphic homology, which can then be computed using
standard methods. Furthermore, we demonstrate that in the context of non-uniform cubical grids this method significantly improves
currently available algorithms based on uniform cubical grids. |
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