Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology

In this paper, we establish a correspondence between the incrementalalgorithm for computing AT-models [8,9] and the one for computingpersistent homology [6,14,15]. We also present a decremental algorithmfor computing AT-models that allows to extend the persistencecomputation to a wider setting. Finally, we show how to combine incrementaland decremental techniques for persistent homology computation.