Speeding-Up the Dynamic Programming Procedure for the Edit Distance of Two Strings

  • Giuseppe LanciaEmail author
  • Marcello Dalpasso
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1062)


We describe a way to compute the edit distance of two strings without having to fill the whole dynamic programming (DP) matrix, through a sequence of increasing guesses on the edit distance. If the strings share a certain degree of similarity, the edit distance can be quite smaller than the value of non-optimal solutions, and a large fraction (up to 80–90%) of the DP matrix cells do not need to be computed. Including the method’s overhead, this translates into a speedup factor from \(3\times \) up to \(30\times \) in the time needed to find the optimal solution for strings of length about 20,000.


  1. 1.
    Backurs, A., Indyk, P.: Edit distance cannot be computed in strongly subquadratic time (unless SETH is false). SIAM J. Comput. 47(3), 1087–1097 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gotoh, O.: An improved algorithm for matching biological sequences. J. Mol. Biol. 162(3), 705–708 (1982)CrossRefGoogle Scholar
  3. 3.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology, 534 p. Cambridge University Press (1997)Google Scholar
  4. 4.
    Jones, N.C., Pevzner, P.A.: An Introduction to Bioinformatics Algorithms, 456 p. MIT Press (2004)Google Scholar
  5. 5.
    Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Doklady Akademii Nauk SSSR 163(4), 845–848 (1965)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Needleman, S.B., Wunsch, C.D.: A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 48(3), 443–453 (1970)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche, Informatiche e FisicheUniversity of UdineUdineItaly
  2. 2.Dipartimento di Ingegneria dell’InformazioneUniversity of PadovaPadovaItaly

Personalised recommendations