2016/06/01 by Henselman, Gregory, Ghrist, Robert · 2 citations
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1606.00199
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here presented rely on a novel relationship between discrete Morse theory, matroid theory, and classical matrix factorizations. We provide background, detail the algorithms, and benchmark the software implementation in the Eirene package.