Computing Persistent Homology of Flag Complexes via Strong Collapses

Jean-Daniel Boissonnat (1, 2) , Siddharth Pritam (2)

1 CRISAM - Inria Sophia Antipolis - Méditerranée
2 DATASHAPE - Understanding the Shape of Data

This paper is a continuation of the research reported in [7] on the usage of strong collapses to accelerate the computation of persistent homology (PH). We show that further decisive progress can be obtained if one restricts the family of simplicial complexes to flag complexes. The resulting method is simple and extremely efficient.

Mots clés: 2012 ACM Subject Classification Mathematics of computing; Topological Data Analysis; Computational geometry Keywords and phrases Computational Topology; Strong Collapse; Persistent homology

Domaines: Géométrie algorithmique [cs.CG]; Algorithme et structure de données [cs.DS]; Topologie algébrique [math.AT]; Topologie géométrique [math.GT]

Jean-Daniel Boissonnat, Siddharth Pritam. Computing Persistent Homology of Flag Complexes via Strong Collapses. 2018. ⟨hal-01950074⟩