A Theory of Sub-Barcodes

@article{Chubet2022ATO,
  title={A Theory of Sub-Barcodes},
  author={Oliver A. Chubet and Kirk P. Gardner and Don Sheehy},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.10504}
}
From the work of Bauer and Lesnick, it is known that there is no functor from the category of pointwise finite-dimensional persistence modules to the category of barcodes and overlap matchings . In this work, we introduce sub-barcodes and show that there is a functor from the category of factorizations of persistence module homomorphisms to a poset of barcodes ordered by the sub-barcode relation . Sub-barcodes and factorizations provide a looser alternative to bottleneck matchings and… 

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Maximum Subbarcode Matching and Subbarcode Distance

The subbarcode matching algorithm presented is a gener-alization of the up-right matching algorithm given by Karp et al [11], which has O ( n log n ) runtime, where n is the number of distinct intervals in the barcodes.

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