A fast bit-vector algorithm for approximate string matching based on dynamic programming

Abstract

The approximate string matching problem is to find all locations at which a query of length m matches a substring of a text of length n with k-or-fewer differences. Simple and practical bit-vector algorithms have been designed for this problem, most notably the one used in agrep. These algorithms compute a bit representation of the current state-set of the k-difference automaton for the query, and asymptotically run in O(nmk/w) time where w is the word size of the machine (e.g. 32 or 64 in practice). Here we present an algorithm of comparable simplicity that requires only O(nm/w) time by virtue of computing a bit representation of the relocatable dynamic programming matrix for the problem. Thus the algorithm's performance is independent of k, and it is found to be more efficient than the previous results for many choices of k and small m.Moreover, because the algorithm is not dependent on k, it can be used to rapidly compute blocks of the dynamic programming matrix as in the 4-Russians algorithm of Wu, Manber, and Myers. This gives rise to an O(kn/w) expected-time algorithm for the case where m may be arbitrarily large. In practice this new algorithm, which computes a region of the d.p. matrix in 1 x w blocks using the basic algorithm as a subroutine, is significantly faster than our previous 4-Russians algorithm, which computes the same region in 1 x 5 blocks using table lookup. This performance improvement yields a code which is superior to all existing algorithms except for some filtration algorithms that are superior when k/m is sufficiently small.KeywordsBasic AlgorithmTable LookupEdit DistanceString MatchApproximate String MatchThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.