We present a new reduction algorithm for the efficient computation of the homology of a cubical set. The algorithm is based on constructing a possibly large acyclic subspace, and then computing the relative homology instead of the plain homology. We show that the construction of acyclic subspace may be performed in linear time. This significantly reduces the amount of data that needs to be processed in the algebraic way, and in practice it proves itself to be significantly more efficient than other available cubical homology algorithms.

Abstract. Homology computations recently gain vivid attention in science. New methods, enabling fast and memory efficient computations are needed in order to process large simplicial complexes. In this paper we present the acyclic subspace reduction algorithm adapted to simplical complexes. It provides fast and memory efficient preprocessing of the given data. A variant of the method for distributed computations is also presented.