Parallel Computation of Persistent Homology using the Blowup Complex

Conference · Mon Apr 27 00:00:00 EDT 2015

DOI:https://doi.org/10.1145/2755573.2755587· OSTI ID:1235080

Lewis, Ryan ^[1]; Morozov, Dmitriy ^[2]

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1. Stanford Univ., CA (United States)
2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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 operation, 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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States), Computational Research Division
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 1235080
• Report Number(s): LBNL-177165; ir:177165
• Resource Relation: Conference: 27. ACM symposium on parallelism in algorithms and architectures (SPAA15), Portland, OR (United States), 13-15 Jun 2015
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING