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DOI: 10.4230/LIPIcs.CPM.2024.14
When Is the Normalized Edit Distance over Non-Uniform Weights a Metric?

Authors: Dana Fisman and Ilay Tzarfati

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
The well known Normalized Edit Distance (ned) [Marzal and Vidal 1993] is known to disobey the triangle inequality on contrived weight functions, while in practice it often exhibits a triangular behavior. Let d be a weight function on basic edit operations, and let ned_{d} be the resulting normalized edit distance. The question what criteria should d satisfy for ned_{d} to be a metric is long standing. It was recently shown that when d is the uniform weight function (all operations cost 1 except for no-op which costs 0) then ned_{d} is a metric. The question regarding non-uniform weights remained open. In this paper we answer this question by providing a necessary and sufficient condition on d under which ned_{d} is a metric.
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Dana Fisman and Ilay Tzarfati. When Is the Normalized Edit Distance over Non-Uniform Weights a Metric?. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fisman_et_al:LIPIcs.CPM.2024.14,
  author =	{Fisman, Dana and Tzarfati, Ilay},
  title =	{{When Is the Normalized Edit Distance over Non-Uniform Weights a Metric?}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.14},
  URN =		{urn:nbn:de:0030-drops-201247},
  doi =		{10.4230/LIPIcs.CPM.2024.14},
  annote =	{Keywords: Normalized Edit Distance, Non-uniform Weights, Triangle Inequality, Metric}
}
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