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When Is the Normalized Edit Distance over Non-Uniform Weights a Metric?

Authors Dana Fisman , Ilay Tzarfati

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Author Details

Dana Fisman
  • Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
Ilay Tzarfati
  • Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel

Funding

  • Tzarfati, Ilay: Supported by ISF grant 2507/21 and Frankel Center for Computer Science, BGU.

Acknowledgements

We would like to thank Oded Margalit, Elina Sudit and Sandra Zilles for comments on an earlier draft of this paper.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.CPM.2024.14

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation → Formal languages and automata theory
Keywords
  • Normalized Edit Distance
  • Non-uniform Weights
  • Triangle Inequality
  • Metric

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