文章基本信息

标题：The Reeb Graph Edit Distance Is Universal
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作者：Ulrich Bauer ; Claudia Landi ; Facundo Mmoli 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：164
页码：15:1-15:16
DOI：10.4230/LIPIcs.SoCG.2020.15
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal.
关键词：Reeb graphs; topological descriptors; edit distance; interleaving distance