Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Simplification of complexes for persistent homology computations

Pages: 49 – 63

DOI: https://dx.doi.org/10.4310/HHA.2014.v16.n1.a3

Authors

Paweł Dłotko (Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.; Institute of Computer Science, Jagiellonian University, Krakow, Poland)

Hubert Wagner (Institute of Computer Science, Jagiellonian University, Krakow, Poland)

Abstract

In this paper we focus on preprocessing for persistent homology computations. We adapt some techniques that were successfully used for standard homology computations. The main idea is to reduce the complex prior to generating its boundary matrix, which is costly to store and process. We discuss the following reduction methods: elementary collapses, coreductions (as defined by Mrozek and Batko), and acyclic subspace methods (introduced by Mrozek, Pilarczyk, and Żelazna).

Keywords

homology, persistence, reduction algorithm

2010 Mathematics Subject Classification

55-04, 55U05, 57M15, 68R05

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Published 2 June 2014