Parallel Computation of Persistent Homology using the Blowup Complex

Ryan Lewis, Dmitriy Morozov
2015 Proceedings of the 27th ACM on Symposium on Parallelism in Algorithms and Architectures - SPAA '15  
We describe a parallel algorithm that computes persistent homology, an algebraic descriptor of a filtered topological space. Our algorithm is distinguished by operating on a spatial decomposition of the domain, as opposed to a decomposition with respect to the filtration. We rely on a classical construction, called the Mayer-Vietoris blowup complex, to glue global topological information about a space from its disjoint subsets. We introduce an efficient algorithm to perform this gluing
more » ... , which may be of independent interest, and describe how to process the domain hierarchically. We report on a set of experiments that help assess the strengths and identify the limitations of our method.
doi:10.1145/2755573.2755587 dblp:conf/spaa/LewisM15 fatcat:3cm3m2q4e5fqzbb7zj6yt6j7am