Algorithmic decomposition of filtered chain complexes
Year: 2020
Type: preprint
Abstract: We present an algorithm to decompose filtered chain complexes into sums of interval spheres. The algorithm's correctness is proved through principled methods from homotopy theory. Its asymptotic runtime complexity is shown to be cubic in the number of generators, e.g. the simplices of a simplicial complex, as it is based on the row reduction of the boundary matrix by Gaussian elimination. Applying homology to a filtered chain complex, one obtains a persistence module. So our method also provides a new algorithm for the barcode decomposition of persistence modules. The key differences with respect to the state-of-the-art persistent homology algorithms are that our algorithm uses row rather than column reductions, it intrinsically adopts both the clear and compress optimisation strategies, and, finally, it can process rows according to any random order.
Source: arXiv (Cornell University)
Authors: Wojciech Chachólski, Barbara Giunti, Alvin Jin, Claudia Landi
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3108143919