2023/11/02 by Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, di Montesano, Sebastiano Cultrera +5
Computer Science · Mathematics · #Algorithm #Biology #Combinatorics #Computational Geometry (cs.CG) #Computational biology #Computer science #Data Structures and Algorithms (cs.DS) #Data Visualization and Analytics #Data structure #Database #Diagram #FOS: Computer and information sciences #Genetics #Homology (biology) #Mathematics #Paleontology #Persistent homology #Programming language #Representation (politics) #Series (stratigraphy) #Theoretical computer science #Time Series Analysis and Forecasting #Topological and Geometric Data Analysis #Tree (set theory)
paper · pdf · doi:10.48550/arxiv.2311.01115
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right.