Coreduction Homology Algorithm for Regular CW-Complexes

Authors:
Paweł Dłotko;Tomasz Kaczynski;Marian Mrozek;Thomas Wanner
Affiliations:
Jagiellonian University, Institute of Computer Science, ul. St. Łojasiewicza 6, 30-348, Kraków, Poland;Université de Sherbrooke, Département de Mathématiques, J1K 2R1, Sherbrooke, Québec, Canada;Jagiellonian University, Institute of Computer Science, ul. St. Łojasiewicza 6, 30-348, Kraków, Poland and WSB-NLU, Division of Computational Mathematics, ul. Zielona 27, 33-300, Now ...;George Mason University, Department of Mathematical Sciences, 22030, Fairfax, VA, USA
Venue:
Discrete & Computational Geometry
Year:
2011

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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.