Chunk Reduction for Multi-Parameter Persistent Homology

Ulderico Fugacci, Michael Kerber

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

Abstract

The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an important pre-processing step consists of simplifying the input while maintaining the homological information. We present an algorithm that drastically reduces the size of an input. Our approach is an extension of the chunk algorithm for persistent homology (Bauer et al., Topological Methods in Data Analysis and Visualization III, 2014). We show that our construction produces the smallest multi-filtered chain complex among all the complexes quasi-isomorphic to the input, improving on the guarantees of previous work in the context of discrete Morse theory. Our algorithm also offers an immediate parallelization scheme in shared memory. Already its sequential version compares favorably with existing simplification schemes, as we show by experimental evaluation.
Original languageEnglish
Title of host publication35th International Symposium on Computational Geometry, SoCG 2019, June 18-21, 2019, Portland, Oregon, USA
Pages37:1-37:14
Number of pages14
Publication statusPublished - 2019
Event35th International Symposium on Computational Geometry - Portland, United States
Duration: 18 Jun 201921 Jun 2019

Conference

Conference35th International Symposium on Computational Geometry
Abbreviated titleSoCG 2019
CountryUnited States
CityPortland
Period18/06/1921/06/19

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Cite this

Fugacci, U., & Kerber, M. (2019). Chunk Reduction for Multi-Parameter Persistent Homology. In 35th International Symposium on Computational Geometry, SoCG 2019, June 18-21, 2019, Portland, Oregon, USA (pp. 37:1-37:14)

Chunk Reduction for Multi-Parameter Persistent Homology. / Fugacci, Ulderico; Kerber, Michael.

35th International Symposium on Computational Geometry, SoCG 2019, June 18-21, 2019, Portland, Oregon, USA. 2019. p. 37:1-37:14.

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

Fugacci, U & Kerber, M 2019, Chunk Reduction for Multi-Parameter Persistent Homology. in 35th International Symposium on Computational Geometry, SoCG 2019, June 18-21, 2019, Portland, Oregon, USA. pp. 37:1-37:14, 35th International Symposium on Computational Geometry, Portland, United States, 18/06/19.
Fugacci U, Kerber M. Chunk Reduction for Multi-Parameter Persistent Homology. In 35th International Symposium on Computational Geometry, SoCG 2019, June 18-21, 2019, Portland, Oregon, USA. 2019. p. 37:1-37:14
Fugacci, Ulderico ; Kerber, Michael. / Chunk Reduction for Multi-Parameter Persistent Homology. 35th International Symposium on Computational Geometry, SoCG 2019, June 18-21, 2019, Portland, Oregon, USA. 2019. pp. 37:1-37:14
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