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Title: Parallel Computation of Persistent Homology using the Blowup Complex

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.
Authors:
 [1] ;  [2]
  1. Stanford Univ., CA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
OSTI Identifier:
1235080
Report Number(s):
LBNL--177165
ir:177165
DOE Contract Number:
AC02-05CH11231
Resource Type:
Conference
Resource Relation:
Conference: 27. ACM symposium on parallelism in algorithms and architectures (SPAA15), Portland, OR (United States), 13-15 Jun 2015
Research Org:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States), Computational Research Division
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING