Homological Trimming and Regularity of Filtrations via Local Obstruction Modules
Abstract
Existing link-based combinatorial preprocessing methods speed up the computation of persistent homology by removing a vertex or edge only when its link remains a cone. We replace this condition with a quantitative homological certificate. The reduced homology of the filtered link of a generator (a vertex or edge) defines a local obstruction module whose future part describes the effect of deleting that generator. Its barcode certifies either exact deletion or an explicit bound on the bottleneck error, and a conflict colouring extends this guarantee to families of generators. Our implementation, HomTrim, removes an additional 13% to 41% of the input edges beyond domination-only preprocessing and reduces backend persistence time by factors ranging from 1.55 to 4.61 on weighted flag filtrations. The same module also yields regularity diagrams that measure how far a generator can move before becoming visible to homology, together with a multiscale stability result.
Related
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BibTeX
@misc{pritam2026homological,
title = {{Homological Trimming and Regularity of Filtrations via Local Obstruction Modules}},
author = {Siddharth Pritam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28160},
eprint = {2609.28160},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28160},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Homological Trimming and Regularity of Filtrations via Local Obstruction Modules
AU - Siddharth Pritam
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28160
UR - https://arxiv.org/abs/2609.28160
AB - Existing link-based combinatorial preprocessing methods speed up the computation of persistent homology by removing a vertex or edge only when its link remains a cone. We replace this condition with a quantitative homological certificate. The reduced homology of the filtered link of a generator (a vertex or edge) defines a local obstruction module whose future part describes the effect of deleting that generator. Its barcode certifies either exact deletion or an explicit bound on the bottleneck error, and a conflict colouring extends this guarantee to families of generators. Our implementation, HomTrim, removes an additional 13% to 41% of the input edges beyond domination-only preprocessing and reduces backend persistence time by factors ranging from 1.55 to 4.61 on weighted flag filtrations. The same module also yields regularity diagrams that measure how far a generator can move before becoming visible to homology, together with a multiscale stability result.
ER -