A. Zomorodian, G. Carlsson, Computing Persistent Homology, Proc. Symp. Comput. Geom. (2004), pp. 347-356.


We study the homology of a filtered d-dimensional simplicial complex K as a single algebraic entity and establish a correspondence that provides a simple description over fields. Our analysis enables us to derive a natural algorithm for computing persistent homology over an arbitrary field in any dimension. Our study also implies the lack of a simple classification over non-fields. Instead, we give an algorithm for computing individual persistent homology groups over an arbitrary PIDs in any dimension.


  title = "Computing Persistent Homology", 
  author = "Zomorodian, A. and Carlsson, G.",
  booktitle = "Proc. 20th Ann. ACM Sympos. Comput. Geom.",
  year = 2004,
  pages = 347--356,