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The Normalized Edit Distance with Uniform Operation Costs Is a Metric

Authors: Dana Fisman, Joshua Grogin, Oded Margalit, and Gera Weiss

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)


Abstract
We prove that the normalized edit distance proposed in [Marzal and Vidal 1993] is a metric when the cost of all the edit operations are the same. This closes a long standing gap in the literature where several authors noted that this distance does not satisfy the triangle inequality in the general case, and that it was not known whether it is satisfied in the uniform case - where all the edit costs are equal. We compare this metric to two normalized metrics proposed as alternatives in the literature, when people thought that Marzal’s and Vidal’s distance is not a metric, and identify key properties that explain why the original distance, now known to also be a metric, is better for some applications. Our examination is from a point of view of formal verification, but the properties and their significance are stated in an application agnostic way.

Cite as

Dana Fisman, Joshua Grogin, Oded Margalit, and Gera Weiss. The Normalized Edit Distance with Uniform Operation Costs Is a Metric. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 17:1-17:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{fisman_et_al:LIPIcs.CPM.2022.17,
  author =	{Fisman, Dana and Grogin, Joshua and Margalit, Oded and Weiss, Gera},
  title =	{{The Normalized Edit Distance with Uniform Operation Costs Is a Metric}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.17},
  URN =		{urn:nbn:de:0030-drops-161446},
  doi =		{10.4230/LIPIcs.CPM.2022.17},
  annote =	{Keywords: edit distance, normalized distance, triangle inequality, metric}
}
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