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  • 标题:Computing Bottleneck Distance for 2-D Interval Decomposable Modules
  • 作者:Tamal K. Dey ; Cheng Xin
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2018
  • 卷号:99
  • 页码:32:1-32:15
  • DOI:10.4230/LIPIcs.SoCG.2018.32
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For 1-D persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck distance with known efficient algorithms. The question is open for most n-D persistence modules, n>1, because of the well recognized complications of the indecomposables. Here, we consider a reasonably complicated class called 2-D interval decomposable modules whose indecomposables may have a description of non-constant complexity. We present a polynomial time algorithm to compute the bottleneck distance for these modules from indecomposables, which bounds the interleaving distance from above, and give another algorithm to compute a new distance called dimension distance that bounds it from below.
  • 关键词:Persistence modules; bottleneck distance; interleaving distance
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