Pruning vineyards: updating barcodes by removing simplices
| Autor: | Giunti, Barbara, Lazovskis, Jānis |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The barcode computation of a filtration can be computationally expensive. Therefore, it is useful to have methods to update a barcode if the associated filtration undergoes small changes, such as changing the entrance order, or adding and removing simplices. There is already a rich literature on how to efficiently update a barcode in the first two cases, but the latter case has not been investigated yet. In this work, we provide an algorithm to update a reduced boundary matrix when simplices are removed. We show that the complexity of this algorithm is lower than recomputing the barcode from scratch, with both theoretical and experimental methods. Comment: 14 pages, 9 figures |
| Databáze: | arXiv |
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