@inproceedings{f0b2aa4ab53a4dd0a78cea6bf188725d,

title = "When Is the Normalized Edit Distance over Non-Uniform Weights a Metric?",

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 nedd be the resulting normalized edit distance. The question what criteria should d satisfy for nedd 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 nedd 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 nedd is a metric.",

keywords = "Metric, Non-uniform Weights, Normalized Edit Distance, Triangle Inequality",

author = "Dana Fisman and Ilay Tzarfati",

note = "Publisher Copyright: {\textcopyright} Dana Fisman and Ilay Tzarfati.; 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 ; Conference date: 25-06-2024 Through 27-06-2024",

year = "2024",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.CPM.2024.14",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Shunsuke Inenaga and Puglisi, {Simon J.}",

booktitle = "35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024",

address = "Germany",

}