We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

Computing Interleaving and Bottleneck Distance for 2-D Interval Decomposable Modules

Formale Metadaten

Titel
Computing Interleaving and Bottleneck Distance for 2-D Interval Decomposable Modules
Serientitel
Anzahl der Teile
19
Autor
Mitwirkende
Lizenz
CC-Namensnennung - keine kommerzielle Nutzung - keine Bearbeitung 4.0 International:
Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nicht-kommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
Identifikatoren
Herausgeber
Erscheinungsjahr
Sprache

Inhaltliche Metadaten

Fachgebiet
Genre
Abstract
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 {\em 2-D interval decomposable} modules whose indecomposables may have a description of non-constant complexity. We present a polynomial time algorithm to compute the interleaving distance between two such indecomposables. This leads to a polynomial time algorithm for computing the bottleneck distance between two 2-D interval decomposable modules, which bounds their interleaving distance from above. We give another algorithm to compute a new distance called {\em dimension distance} that bounds it from below.