TY - CHAP
AB - We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.
AU - Bauer, Ulrich
AU - Kerber, Michael
AU - Reininghaus, Jan
ED - Bremer, Peer-Timo
ED - Hotz, Ingrid
ED - Pascucci, Valerio
ED - Peikert, Ronald
ID - 2044
T2 - Topological Methods in Data Analysis and Visualization III
TI - Clear and Compress: Computing Persistent Homology in Chunks
ER -