---
res:
  bibo_abstract:
  - 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) Γ R d (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
    in the complex, d its dimension, and R d (n) is the complexity of computing the
    rank of an n × n matrix with O (d n) nonzero entries. Depending on the choice
    of the rank algorithm, this yields a deterministic O (C (1 - δ) Γ n 2.376) algorithm,
    an O (C (1 - δ) Γ n 2.28) Las-Vegas algorithm, or an O (C (1 - δ) Γ n 2 + ε{lunate})
    Monte-Carlo algorithm for an arbitrary ε{lunate} > 0. The space complexity
    of the Monte-Carlo version is bounded by O (d n) = O (n log n).@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Chao
      foaf_name: Chen, Chao
      foaf_surname: Chen
      foaf_workInfoHomepage: http://www.librecat.org/personId=3E92416E-F248-11E8-B48F-1D18A9856A87
  - foaf_Person:
      foaf_givenName: Michael
      foaf_name: Kerber, Michael
      foaf_surname: Kerber
      foaf_workInfoHomepage: http://www.librecat.org/personId=36E4574A-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-8030-9299
  bibo_doi: 10.1016/j.comgeo.2012.02.010
  bibo_issue: '4'
  bibo_volume: 46
  dct_date: 2013^xs_gYear
  dct_identifier:
  - UT:000314437000004
  dct_language: eng
  dct_publisher: Elsevier@
  dct_title: An output sensitive algorithm for persistent homology@
...