Interleaved computation for persistent homology

TL;DR

This paper introduces an interleaved computation method for persistent homology that manages memory efficiently and updates the computational state dynamically as new edges are added, improving speed and complexity.

Contribution

The paper presents a novel interleaved algorithm for persistent homology that handles bounded memory and updates the computation incrementally.

Findings

The method reduces memory usage during persistent homology computation.

It improves computational speed and complexity over traditional methods.

The approach effectively updates the persistence algorithm with new data.

Abstract

We describe an approach to bounded-memory computation of persistent homology and betti barcodes, in which a computational state is maintained with updates introducing new edges to the underlying neighbourhood graph and percolating the resulting changes into the simplex stream feeding the persistence algorithm. We further discuss the memory consumption and resulting speed and complexity behaviours of the resulting algorithm.