Interleaved computation for persistent homology
  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. 
Mikael Vejdemo-Johansson
cs.CG math.AT