We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices according to each case. We conclude with some future work directions and open problems.

Motivation: This article presents a method for assembling shotgun sequences which primarily uses high confidence regions whilst taking advantage of additional available information such as low confidence regions, quality values or repetitive region tags. Conflict situations are resolved with routines for analysing trace signals.

This paper describes a generic model of matching that can be usefully applied to misuse intrusion detection. The model is based on Colored Petri Nets. Guards define the context in which signatures are matched. The notion of start and final states, and paths between them define the set of event sequences matched by the net. Partial order matching can also be specified in this model. The main benefits of the model are its generality, portability and flexibility.

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 either O(nmk/w) orO(nm log �/w) time where w is the word size of the machine (e.g., 32 or 64 in practice), and � is the size of the pattern alphabet. 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 et al. [1996]. 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, that computes a region of the dynamic programming (d.p.) matrix w entries at a time using the basic algorithm as a subroutine, is significantly faster than our previous 4-Russians algorithm, that computes the same region 4 or 5 entries at a time using table lookup. This performance improvement yields a code that is either superior or competitive with all existing algorithms except for some filtration algorithms that are superior when k/m is sufficiently small.

... text. When searching complex or approximate patterns, our algorithms are up to 8 times faster than the search on uncompressed text. We also discuss the impact of our technique in inverted files pointing to logical blocks and argue for the possibility of keeping the text compressed all the time, decompressing only for displaying purposes.

. We present in this paper two algorithms. The first one extracts repeated motifs from a sequence defined over an alphabet \Sigma . For instance, \Sigma may be equal to fA, C, G, Tg and the sequence represents an encoding of a DNA macromolecule. The motifs searched correspond to words over the same alphabet which occur a minimum number q of times in the sequence with at most e mismatches each time (q is called the quorum constraint). The second algorithm extracts common motifs from a set of N 2 sequences. In this case, the motifs must occur, again with at most e mismatches, in 1 q N distinct sequences of the set. In both cases, the words representing the motifs may never be present exactly in the sequences. We therefore speak of the motifs, repeated in a sequence or common to a set of them, as being "external" objects and denote them by the expression "valid models" if they verify the quorum constraint q. The approach we introduce here for finding all valid models corr...

We present a new algorithm for on-line approximate string matching. The algorithm is based on the simulation of a non-deterministic finite automaton built from the pattern and using the text as input. This simulation uses bit operations on a RAM machine with word length w = \Omega\Gamma137 n) bits, where n is the text size. This is essentially similar to the model used in Wu and Manber's work, although we improve the search time by packing the automaton states differently. The running time achieved is O(n) for small patterns (i.e. whenever mk = O(log n)), where m is the pattern length and k ! m the number of allowed errors. This is in contrast with the result of Wu and Manber, which is O(kn) for m = O(log n). Longer patterns can be processed by partitioning the automaton into many machine words, at O(mk=w n) search cost. We allow generalizations in the pattern, such as classes of characters, gaps and others, at essentially the same search cost. We then explore other novel techniques t...

... In this paper we merge bit-parallelism and suffix automata, so that a nondeterministic suffix automaton is simulated using bit-parallelism. The resulting algorithm, called BNDM, obtains the best from both worlds. It is much simpler to implement than BDM and nearly as simple as Shift-Or. It inherits from Shift-Or the ability to handle flexible patterns and from BDM the ability to skip characters. BNDM is 30%-40% faster than BDM and up to 7 times faster than Shift-Or. When compared to the fastest existing algorithms on exact patterns (which belong to the BM family), BNDM is from 20% slower to 3 times faster, depending on the alphabet size. With respect to flexible pattern searching, BNDM is by far the fastest technique to deal with classes of characters and is competitive to search allowing errors. In particular, BNDM seems very adequate for computational biology applications, since it is the fastest algorithm to search on DNA sequences and flexible searching is an important problem in that

We present new algorithms for approximate string matching based in simple, but efficient, ideas. First, we present an algorithm for string matching with mismatches based in arithmetical operations that runs in linear worst case time for most practical cases. This is a new approach to string searching. Second, we present an algorithm for string matching with errors based on partitioning the pattern that requires linear expected time for typical inputs. 1 Introduction Approximate string matching is one of the main problems in combinatorial pattern matching. Recently, several new approaches emphasizing the expected search time and practicality have appeared [3, 4, 27, 32, 31, 17], in contrast to older results, most of them are only of theoretical interest. Here, we continue this trend, by presenting two new simple and efficient algorithms for approximate string matching. First, we present an algorithm for string matching with k mismatches. This problem consists of finding all instances o...

Given a text of length n and a query of length q, we present an algorithm for finding all locations of m-tuples in the text and in the query that differ by at most k mismatches. This problem is motivated by the dot-matrix constructions for sequence comparison and optimal oligonucleotide probe selection routinely used in molecular biology. In the case q = m the problem coincides with the classical approximate string matching with k mismatches problem. We present a new approach to this problem based on multiple hashing, which may have advantages over some sophisticated and theoretically efficient methods that have been proposed. This paper describes a two-stage process. The first stage (multiple filtration) uses a new technique to preselect roughly similar m-tuples. The second stage compares these m-tuples using an accurate method. We demonstrate the advantages of multiple filtration in comparison with other techniques for approximate pattern matching.