Coreduction homology algorithm for inclusions and persistent homology

48. Marian Mrozek, Thomas Wanner:
    Coreduction homology algorithm for inclusions and persistent homology
    Computers & Mathematics with Applications 60(10), pp. 2812-2833, 2010.

Abstract

We present an algorithm for computing the homology of inclusion maps which is based on the idea of coreductions and leads to significant speed improvements over current algorithms. It is shown that this algorithm can be extended to compute both persistent homology and an extension of the persistence concept to two-sided filtrations. In addition to describing the theoretical background, we present results of numerical experiments, as well as several applications to concrete problems in materials science.

Links

The published version of the paper can be found at https://doi.org/10.1016/j.camwa.2010.09.036.

Bibtex

@article{mrozek:wanner:10a,
   author = {Marian Mrozek and Thomas Wanner},
   title = {Coreduction homology algorithm for inclusions and
            persistent homology},
   year = 2010,
   journal = {Computers \& Mathematics with Applications},
   volume = 60,
   number = 10,
   pages = {2812--2833},
   doi = {10.1016/j.camwa.2010.09.036}
   }