### Abstract

Original language | English |
---|---|

Title of host publication | 33rd International Symposium on Computational Geometry (SoCG 2017) |

Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH |

Pages | 57:1-57:16 |

Number of pages | 16 |

Volume | 77 |

Edition | LIPICS |

ISBN (Electronic) | 978-3-95977-038-5 |

Publication status | Published - 2017 |

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### Fields of Expertise

- Information, Communication & Computing

### Cite this

*33rd International Symposium on Computational Geometry (SoCG 2017)*(LIPICS ed., Vol. 77, pp. 57:1-57:16). Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH.

**Barcodes of Towers and a Streaming Algorithm for Persistent Homology.** / Kerber, Michael; Schreiber, Hannah.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*33rd International Symposium on Computational Geometry (SoCG 2017).*LIPICS edn, vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, pp. 57:1-57:16.

}

TY - GEN

T1 - Barcodes of Towers and a Streaming Algorithm for Persistent Homology

AU - Kerber, Michael

AU - Schreiber, Hannah

PY - 2017

Y1 - 2017

N2 - A tower is a sequence of simplicial complexes connected by simplicial maps. We show how to compute a filtration, a sequence of nested simplicial complexes, with the same persistent barcode as the tower. Our approach is based on the coning strategy by Dey et al. (SoCG 2014). We show that a variant of this approach yields a filtration that is asymptotically only marginally larger than the tower and can be efficiently computed by a streaming algorithm, both in theory and in practice. Furthermore, we show that our approach can be combined with a streaming algorithm to compute the barcode of the tower via matrix reduction. The space complexity of the algorithm does not depend on the length of the tower, but the maximal size of any subcomplex within the tower. Experimental evaluations show that our approach can efficiently handle towers with billions of complexes.

AB - A tower is a sequence of simplicial complexes connected by simplicial maps. We show how to compute a filtration, a sequence of nested simplicial complexes, with the same persistent barcode as the tower. Our approach is based on the coning strategy by Dey et al. (SoCG 2014). We show that a variant of this approach yields a filtration that is asymptotically only marginally larger than the tower and can be efficiently computed by a streaming algorithm, both in theory and in practice. Furthermore, we show that our approach can be combined with a streaming algorithm to compute the barcode of the tower via matrix reduction. The space complexity of the algorithm does not depend on the length of the tower, but the maximal size of any subcomplex within the tower. Experimental evaluations show that our approach can efficiently handle towers with billions of complexes.

M3 - Conference contribution

VL - 77

SP - 57:1-57:16

BT - 33rd International Symposium on Computational Geometry (SoCG 2017)

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH

ER -