---
res:
  bibo_abstract:
  - 'We consider the problem of deciding whether the persistent homology group of
    a simplicial pair (K, L) can be realized as the homology H* (X) of some complex
    X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded
    in ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel
    sets of scalar functions on S3 within a given tolerance constraint. This problem
    has relevance to the visualization of medical images by isosurfaces. We also show
    an implication to the theory of well groups of scalar functions: not every well
    group can be realized by some level set, and deciding whether a well group can
    be realized is NP-hard.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Dominique
      foaf_name: Attali, Dominique
      foaf_surname: Attali
  - foaf_Person:
      foaf_givenName: Ulrich
      foaf_name: Bauer, Ulrich
      foaf_surname: Bauer
      foaf_workInfoHomepage: http://www.librecat.org/personId=2ADD483A-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-9683-0724
  - foaf_Person:
      foaf_givenName: Olivier
      foaf_name: Devillers, Olivier
      foaf_surname: Devillers
  - foaf_Person:
      foaf_givenName: Marc
      foaf_name: Glisse, Marc
      foaf_surname: Glisse
  - foaf_Person:
      foaf_givenName: André
      foaf_name: Lieutier, André
      foaf_surname: Lieutier
  bibo_doi: 10.1145/2462356.2462373
  dct_date: 2013^xs_gYear
  dct_language: eng
  dct_publisher: ACM@
  dct_title: Homological reconstruction and simplification in R3@
...