Barcodes of Towers and a Streaming Algorithm for Persistent Homology

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

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.
Original languageEnglish
Title of host publication33rd International Symposium on Computational Geometry (SoCG 2017)
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH
Pages57:1-57:16
Number of pages16
Volume77
EditionLIPICS
ISBN (Electronic)978-3-95977-038-5
Publication statusPublished - 2017

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Towers

Fields of Expertise

  • Information, Communication & Computing

Cite this

Kerber, M., & Schreiber, H. (2017). Barcodes of Towers and a Streaming Algorithm for Persistent Homology. In 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.

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Kerber, M & Schreiber, H 2017, Barcodes of Towers and a Streaming Algorithm for Persistent Homology. in 33rd International Symposium on Computational Geometry (SoCG 2017). LIPICS edn, vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, pp. 57:1-57:16.
Kerber M, Schreiber H. Barcodes of Towers and a Streaming Algorithm for Persistent Homology. In 33rd International Symposium on Computational Geometry (SoCG 2017). LIPICS ed. Vol. 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH. 2017. p. 57:1-57:16
Kerber, Michael ; Schreiber, Hannah. / Barcodes of Towers and a Streaming Algorithm for Persistent Homology. 33rd International Symposium on Computational Geometry (SoCG 2017). Vol. 77 LIPICS. ed. Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, 2017. pp. 57:1-57:16
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