文章基本信息

标题：A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression
本地全文：下载
作者：Danny Hermelin ; Gad M. Landau ; Shir Landau 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2009
卷号：3
页码：529-540
DOI：10.4230/LIPIcs.STACS.2009.1804
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Edit distance; Straight-line Programs; Dynamic programming acceleration via compression; Combinatorial pattern matching