期刊
PROCEEDINGS OF THE TWENTY-FIFTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SCG'09)
卷 -, 期 -, 页码 247-256出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/1542362.1542408
关键词
Zigzag persistent homology; Mayer-Vietoris pyramid; levelset zigzag; extended persistence; algorithms
We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived from the levelsets of a real-valued function on a topological space. The result is a local, symmetric interval descriptor of the function. Our structural results establish a connection between the zigzag pairs in this sequence and extended persistence, and in the process resolve an open question associated with the latter. Our algorithmic results not only provide a way to compute zigzag persistence for any sequence of homology groups, but combined with our structural results give a novel algorithm for computing extended persistence. This algorithm is easily parallelizable and uses (asymptotically) less memory.
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