Bulletin of Mathematical Biology

, Volume 46, Issue 2, pp 327–332 | Cite as

Properties of levenshtein metrics on sequences

  • William H. E. Day


Levenshtein dissimilarity measures are used to compare sequences in application areas including coding theory, computer science and macromolecular biology. In general, they measure sequence dissimilarity by the length of a shortest weighted sequence of insertions, deletions and substitutions required, to transform one sequence into another. Those Levenshtein dissimilarity measures based on insertions and deletions are analyzed by a model involving valuations on a partially ordered set. The model reveals structural relationships among poset, valuation and dissimilarity measure. As a consequence, certain Levenshtein dissimilarity measures are shown to be metrics characterized by betweenness properties and computable in terms of well-known measures of sequence similarity.


Dissimilarity Measure Elementary Operation Longe Common Subsequence Lower Valuation Transitive Binary Relation 
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Copyright information

© Society for Mathematical Biology 1984

Authors and Affiliations

  • William H. E. Day
    • 1
  1. 1.Department of Computer ScienceMemorial University of NewfoundlandSt. John'sCanada

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