Homology computations via acyclic subspace

Authors:
Piotr Brendel;Paweł Dłotko;Marian Mrozek;Natalia Żelazna
Affiliations:
Institute of Computer Science, Jagiellonian University, Poland;Institute of Computer Science, Jagiellonian University, Poland;Institute of Computer Science, Jagiellonian University, Poland;Motorola Solutions, Poland
Venue:
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Year:
2012

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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 simplicial complexes. It provides fast and memory efficient preprocessing of the given data. A variant of the method for distributed computations is also presented. As a result, Betti numbers can be effectively computed.