Variations on theme barcode algorithm

In this talk, I will provide an introduction to the standard barcode algorithm and an overview of some of its variants. I will explain what the pivot pairing is and why it provides the barcode, and how it behaves together with the two classical optimizations called clear and compress. I provide some insight into how the sparseness of the matrix can affect efficiency, and discuss the worst-case and average complexity for some special class of inputs. Finally, I will show how to update the reduced matrix so that it encodes the barcode of the original simplicial complex after the removal of some simplices from the latter.