2018/03/07 by Tamal K. Dey, Dey, Tamal K., Cheng Xin +1 · 3 citations
Computer Science · Engineering · Mathematics · #Anomaly Detection Techniques and Applications #Automated Road and Building Extraction #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1803.02869
openalex publication_date 2018/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For 1-parameter persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck distance with known efficient algorithms. The question is open for most n-parameter persistence modules, n>1, because of the well recognized complications of the indecomposables. Here, we consider a reasonably complicated class called \em n-parameter interval decomposable modules whose indecomposables may have a description of non-constant complexity. We present a polynomial time algorithm to compute the bottleneck distance for these modules from indecomposables, which bounds the interleaving distance from above, and give another algorithm to compute a new distance called \em dimension distance that bounds it from below. An earlier version of this paper considered only the 2-parameter interval decomposable modules~\citeDeyCheng18.