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COMPGEOM
2011
ACM

An output-sensitive algorithm for persistent homology

9 years 2 months ago
An output-sensitive algorithm for persistent homology
In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0, 1), the running time is O(C(1−δ)ΓR(n) log n), where C(1−δ)Γ is the number of homology classes with persistence at least (1−δ)Γ, n is the total number of simplices, and R(n) is the complexity of computing the rank of an n×n matrix with O(n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O(C(1−δ)Γn2.376 ) algorithm, a O(C(1−δ)Γn2.28 ) Las-Vegas algorithm, or a O(C(1−δ)Γn2+ǫ ) Monte-Carlo algorithm for an arbitrary ǫ > 0. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical A...
Chao Chen, Michael Kerber
Added 25 Aug 2011
Updated 25 Aug 2011
Type Journal
Year 2011
Where COMPGEOM
Authors Chao Chen, Michael Kerber
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