--- 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@ ...