2024/10/21 by Arnur Nigmetov, Dmitriy Morozov, Nigmetov, Arnur +1 · 1 citation
Computer Science · Mathematics · #55N31 #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2410.16553
openalex publication_date 2024/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to compute in parallel because it relies on global connectivity of the data. We propose a new algorithm to compute persistent cohomology in the distributed setting. It combines domain and range partitioning. The former is used to reduce and sparsify the coboundary matrix locally. After this initial local reduction, we redistribute the matrix across processors for the global reduction. We experimentally compare our cohomology algorithm with DIPHA, the only publicly available code for distributed computation of persistent (co)homology; our algorithm demonstrates a significant improvement in strong scaling.