A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression

Authors Danny Hermelin, Gad M. Landau, Shir Landau, Oren Weimann

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Danny Hermelin
Gad M. Landau
Shir Landau
Oren Weimann

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Danny Hermelin, Gad M. Landau, Shir Landau, and Oren Weimann. A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 529-540, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic-programming solution for this problem computes the edit-distance between a pair of strings of total length $O(N)$ in $O(N^2)$ time. To this date, this quadratic upper-bound has never been substantially improved for general strings. However, there are known techniques for breaking this bound in case the strings are known to compress well under a particular compression scheme. The basic idea is to first compress the strings, and then to compute the edit distance between the compressed strings. As it turns out, practically all known $o(N^2)$ edit-distance algorithms work, in some sense, under the same paradigm described above. It is therefore natural to ask whether there is a single edit-distance algorithm that works for strings which are compressed under any compression scheme. A rephrasing of this question is to ask whether a single algorithm can exploit the compressibility properties of strings under any compression method, even if each string is compressed using a different compression. In this paper we set out to answer this question by using \emph{straight-line programs}. These provide a generic platform for representing many popular compression schemes including the LZ-family, Run-Length Encoding, Byte-Pair Encoding, and dictionary methods. For two strings of total length $N$ having straight-line program representations of total size $n$, we present an algorithm running in $O(n^{1.4}N^{1.2})$ time for computing the edit-distance of these two strings under any rational scoring function, and an $O(n^{1.34}N^{1.34})$-time algorithm for arbitrary scoring functions. This improves on a recent algorithm of Tiskin that runs in $O(nN^{1.5})$ time, and works only for rational scoring functions.
  • Edit distance
  • Straight-line Programs
  • Dynamic programming acceleration via compression
  • Combinatorial pattern matching


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