Papers for

computational topology developers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Homological trimming speeds up persistence computations with error bounds

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.

Wed 23 SeptComputational GeometryData Structures and Algorithms

The gist

Persistent homology helps find shapes and features in data, but it can be slow to compute. This paper introduces a new way to decide which parts of the data can be removed early based on a local mathematical check, speeding up the process while controlling errors. The authors created a tool called HomTrim that cuts down unnecessary parts more than before and makes the calculations faster. They also develop new diagrams showing how stable these data features are over time.

Open → 2609.28160v1