A.V. Aho and M.J. Corasick. Efficient string matching. C. ACM, 18(6):333--340, 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem but the text and pattern are rectangular matrices rather than strings. For simplicity s sake we assume that T is an n Theta n matrix and P is an m Theta m matrix, although our results apply to rectangular matrices as well. Baker [7] and, independently, Bird [8] used the Aho and Corasick [1] dictionary matching algorithm to obtain a O(n log oe) algorithm for the exact two dimensional matching problem. Their model requires a totally ordered alphabet (since it uses the Aho and Corasick algorithm as a subroutine) and so the time is dependent on the alphabet size. For an unbounded ....

A.V. Aho and M.J. Corasick. Efficient string matching. C. ACM, 18(6):333--340, 1975.

....structure to represent Delta such that any changes of Delta can be processed efficiently and, given any text string t, the occurrences of the patterns of Delta in t can be reported efficiently. For the static case in which no insertion or deletion is supported, optimal solutions already exist [1, 5]. These solutions each can build a data structure representing Delta in O(n) time and search a text t in Research supported in part by Hong Kong RGC Grant 338 065 0027 O(jtj tocc) time, where n denotes the total length of patterns in Delta and tocc is the total number of occurrences of the ....

A.V. Aho and M.J. Corasick. Efficient string matching. Communications of the ACM, 18:333-- 340, 1975.

....voices. Furthermore, the user may want to find a musical excerpt that is not at all considered to be melody. Thus, the capability to cope with all possible combinations of the polyphonic source, would be useful. Crawford, Iliopoulos Raman (1998) presented a sketch of an algorithm based on the Aho Corasick (1975) automaton: First an automaton accepting all the prefixes of a pattern is created. Then, at each point of time, all occurrences of the pattern prefixes are monitored; an existing prefix is either extended or voided depending on whether the next symbol occurs at that point of time. The time ....

Aho, A. V. & Corasick, M. J. (1975). Efficient string matching. Communications of the ACM 18(6), 333-- 340.

....periods) of all prefixes of a string is afforded in overall linear time and space. We report one such construction in Figure 1. 1, for the convenience of the reader, but refer for details and proofs of linearity to discussions of failure functions and related constructs such as found in, e.g. [3, 20, 65]. Once the period structure of the pattern is unveiled, this immediately yields a linear time string searching algorithm. The key element of the algorithm is to maintain, during a text scanning, notion of the longest prefix of the pattern matched so far, and use the border table to jump D R A F T ....

A.V. Aho and M.J. Corasick. Efficient string matching. C. ACM, 18(6):333--340, 1975.

....will intersect one primary row, and only one. This intersection will be any row p i , i = 1 : m of the pattern. Hence, we proceed in two stages. First, a multi string searching of strings p i is performed on primary rows, defining a potential matching area. Any multi string searching automaton [1] can be used. We name this automaton automaton A , this stage horizontal or primary search. The second stage checks secondary characters. So far, this slab method does not significantly differ from [2] that provided a good average case: O( n 2 m ) In order to ensure simultaneously an ....

A. V. Aho and M. Corasick. Efficient String Matching. Communications of the ACM, 18(6):333--340, 1975.

....supported by the Israel Ministry of Science and the Arts grant 8560. z Laboratory for Genetic Disease Research, National Center for Human Genome Research, National Institutes of Health, 9000 Rockville Pike, Bethesda, MD 20892, 301) 496 2477 x 202; schaffer nchgr.nih.gov. Aho and Corasick [1] give an automata based algorithm that preprocesses the pattern dictionary in time O(jDj log j Sigmaj) where jDj is the sum of the lengths of all dictionary patterns and j Sigmaj is the alphabet size. Subsequently one can answer a query in time O(jT j log j Sigmaj) The Aho and Corasick algorithm ....

....and match only, but point out that insert and delete are similar to change. The main data structure in our solution is the suffix tree. We briefly define it in the next subsection. 2. 1 Suffix Trees Definition: Let C = fP 1 ; P k g be a set of strings over alphabet Sigma; P i = P i [1] Delta Delta Delta P i [n i ] i = 1; k: A trie of C is a labeled rooted tree where the root represents the null string and every edge is labeled with an element of Sigma. It is defined recursively as follows: Outgoing edges from depth 0 node (root) Let L 0 = k i=1 fP i [1]g. ....

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A.V. Aho and M.J. Corasick. Efficient string matching. Comm. ACM, 18(6):333--340, 1975.

....the same complexity. For completeness sake we present an overview of the AF algorithm. The main idea behind the AF algorithm is linearizing the pattern matrices along the diagonal to produce a dictionary of strings over an alphabet of subrow subcolumn pairs. The Aho and Corasick automaton [1] is then constructed, where every symbol is a subrow subcolumn pair. An input text is similarly linearized along all the diagonals, and the Aho and Corasick automaton is run on the linearized text. Symbol comparisons are done in constant time via lowest common ancestor (LCA) queries on suffix ....

A.V. Aho and M.J. Corasick. Efficient string matching. Comm. ACM, 18(6):333--340, 1975.

....patterns. Query: Text T of length n over alphabet Sigma. Goal: Preprocess D in time as close to linear as possible, and answer a length n query in time as close to O(n tocc) as possible, where tocc is the number of occurrences of dictionary patterns that appear in the text. Aho and Corasick [1] gave an automaton based algorithm that preprocesses the dictionary in time O(d) and answers a query in time O(n tocc) A logarithmic multiple is present for alphabets of unbounded size. Efficient algorithms for a dynamic dictionary appear in [2, 3, 13, 4, 23] As in the indexing case, the ....

A.V. Aho and M.J. Corasick. Efficient string matching. Comm. ACM, 18(6):333--340, 1975.

....possible matches of all k breaks in the text does not exceed 4n. In addition, the total length of all k breaks does not exceed m, since they are all disjoint substrings of the pattern. All exact matches of all k breaks in the text can therefore be found in time O(n m) by a number of methods (e.g. [2, 15]) 2.The total number of marks may not exceed 4n for the following reason. Suppose there are distinct breaks, appearing a 1 ; a times respectively. Since the total number of appearances of each distinct k break does not exceed 2n k , the total number of marks does not exceed 2n k P ....

....P 2k i=1 jB i j) O(m) time by constructing a trie of the strings in S. Note that since each break in S 0 is distinct, the overall number of exact matches of l breaks of S 0 in T is bounded by n, the length of T . These exact matches can be found in O(n P f i=1 jB 0 i j) O(n m) time [2, 15]. Consider an array A of length n, corresponding to the n locations of the text, with A[i] containing the index of the l break of S 0 that exactly matches at location i of T , if any. Partition this array, into n k pieces of size k, i.e. A[1] A[k] A[k 1] A[2k] To simplify ....

A.V. Aho and M.J. Corasick. Efficient string matching. Comm. ACM, 18(6):333--340, 1975.

....in a divide and conquer approach that solved the string matching with mismatches problem for infinite alphabets in time O(n p m log m) The automaton method is a very efficient technique for exact string matching. It was used by [KMP77, BM77] for an O(n) time exact string matching solution. In [AC75] it was extended to finding text locations where any of a given set of patterns match the text in time O(n total length of the patterns output size) Here output size is the number of times a pair (location; pattern) is output. As remarked by Aho and Corasick, this may be more than n, in case ....

....(Details appear in Section 6. The preprocessing time is O(jP j log j Sigmaj) 2. Construct a new n Theta n matrix, TR . TR contains at each location the number of the longest row of P that starts at that location of T . This stage takes O(n 2 ) time by using a slight modification of the [AC75] algorithm. Details appear in Section 6.2) 3. Find all locations [i; j] in T where for all but at most k of the rows P l , l 2 f1; mg, of P , row P l is a prefix of the row represented by TR [i l Gamma 1; j] Call the (at most k) rows where there is no match the error rows. This step is ....

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A.V. Aho and M.J. Corasick. Efficient string matching. C. ACM, 18(6):333--340, 1975.

....of the string composed of the new symbols in the order that their respective rows appear in the pattern. The string matching part can be done in time O(n 2 ) The only question is how to efficiently identify the occurrences of all pattern rows. This was done by using the Aho and Corasick [AC75] dictionary matching algorithm. The Dictionary Matching Problem is the following: Preprocess a dictionary of patterns fP 1 = p 11 Delta Delta Delta p 1m1 ; P 2 = p 21 Delta Delta Delta p 2m2 ; P k = p k1 Delta Delta Delta p kmk g. Subsequently, for every INPUT: Text T = t 1 Delta ....

A.V. Aho and M.J. Corasick. Efficient string matching. Comm. ACM, 18(6):333--340, 1975.

....appears as a result of the complexity of constructing the parameterized suffix tree. Idury and Schaffer [6] considered a generalization of the standard p string matching, namely, dictionary matching under the parameterized pattern matching model. They used a modified Aho Corasick automaton [1] that, again, has a log(j Sigmaj j Pij) multiplicative factor. In this paper, we investigate the alphabet dependence in the complexity of the standard p string matching problem. We provide an algorithm for p string matching that takes time O(n log ) where = min(m; j Pij) Therefore, its ....

....0 Gamma1 , by induction, and by condtion (2) we know that T i k = T i k 0 Gamma1 , thus we can set f k 1 = f k . We modify the KMP algorithm to solve the m matching problem simply by replacing every equality comparison x = y by x = y . Implementation of x = y Construct table A[1]; A[m] where A[i] the largest k; 1 k i, such that p k = p i . If no such k exists then A[i] i. The following subroutines compute p i = t j for j i, and p i = p j for j i. Compare(p i ,t j ) if A[i] i and t j 6= t j Gamma1 ; t j Gammai 1 then return ....

A.V. Aho and M.J. Corasick. Efficient string matching. C. ACM, 18(6):333--340, 1975.

....problems in compressing strings, and in matching large dictionaries of patterns against texts. These two areas of study have an intimately linked history and are amongst the most intensively studied problems in Computer Science. For compression see e.g. 25] and for dictionary matching see e.g. [3, 18, 22, 5, 4]) In this paper, we present the first work optimal algorithms for these problems in a parallel setting. Furthermore, all of our algorithms are fast, working in time logarithmic in the input size. Compression Schemes A wide variety of compression schemes exist in the literature [25] Amongst the ....

....log j Sigmaj multiplicative factor over the bounds above in both the time and the work; here, Sigma is the alphabet set. On this model too, the work bounds of our algorithm are optimal. For the special case when the alphabet size is polynomial in the input size, the classical algorithm of [3] for dictionary matching can be implemented with randomization in O(n) sequential time and space. For this case, we obtain a suboptimal algorithm: our algorithm has an O(log log d) extra factor in the dictionary and text processing work (with no penalties on time) An important task in our ....

[Article contains additional citation context not shown here]

A.V. Aho and M.J. Corasick. Efficient string matching. Communications of the ACM, 18(6):333--340, 1975.

....University of Maryland, College Park, MD 20742; matias umiacs.umd.edu; partially supported by NSF grants CCR 9111348 and CCR 8906949. against all known strings to find ones that are related. Clearly one would like an algorithm which is fast, even given some huge dictionary. Aho and Corasick [1] introduced and solved the exact dictionary matching problem. Given a dictionary D whose characters are taken from the alphabet 6, they preprocess the dictionary in time O(jDj log j6j) and then process text T in time O(jT j log j6j) This result is perhaps surprising because the text scanning ....

....be the size of the dictionary, oe be the effective alphabet, that is, the number of distinct characters that occur in D, t = jT j be the text size, p = jP j be the size of the pattern to be inserted or deleted, and m be the size of the largest pattern in D. Static Dynamic prep. updates d log oe [1] p log d [3] text scan t log oe t log d prep. updates d x2.2 p log k x5.2 Text Scan t t log k prep. updates d x4 p x2.3 text scan t log d mt Table 1. Serial algorithms Static Dynamic prep. time log m log d y update work p log d [3] text time log m log d scan work t log m log d prep. ....

[Article contains additional citation context not shown here]

A. V. Aho and M. J. Corasick. Efficient string matching. Commun. ACM, 18(6):333-- 340, 1975.

....matching problem but the text and pattern are rectangular matrices rather than strings. For simplicity s sake we assume that T is an n2 n matrix and P is an m2m matrix, although our results apply to rectangular matrices as well. Baker [8] and, independently, Bird [9] used the Aho and Corasick [1] dictionary matching algorithm to obtain a O(n 2 log oe) algorithm for the exact two dimensional matching problem. Their model requires a totally ordered alphabet (since it uses the Aho and Corasick algorithm as a subroutine) and so the time is dependent on the alphabet size. For an unbounded ....

A. Aho and M. Corasick, Efficient string matching, C. ACM, 18 (1975), pp. 333--340.

....ABF 94b] we used periodicity to find the first optimal pattern matching algorithm for compressed two dimensional texts. Another application is the two dimensional exact matching problem. Here the text is not compressed. Baker [B 78] and, independently, Bird [Bi 77] used the Aho and Corasick [AC 75] dictionary matching algorithm to obtain a O(n 2 log j Sigmaj) algorithm for this problem. This algorithm is automaton based and therefore the running time of the text scanning phase is dependent on the size of the alphabet. In [ABF 94a] we used periodicity analysis to produce the first two ....

A.V. Aho and M.J. Corasick, "Efficient String Matching", C. ACM, Vol. 18, No. 6, 1975, pp. 333-340.

....In this process, the unit squares will change in a continuous fashion. This includes the boundaries of the unit squares as well as the boundaries of areas within them. Whenever new areas will be formed, we will take note of them. 4.2. A first algorithm The algorithm given by Aho and Corasick [AC7 5], finds all the occurrences of multiple patterns in a given text. It solves the D 1 D problem in O( mm n) time, and the D 2 D problem in O( mm 2 n 2 ) time. Example: Let the continuous pattern consist of four unicolor intervals [0,2.5) 2.5,5.7) 5.7,7.2) 7.2,9) the piling will ....

A.V. Aho and M.J. Corasick, "Efficient String Matching," CACM, Vol. 18, No. 6, 333-340, 1975.

....appears as a result of the complexity of constructing the parameterized suffix tree. Idury and Schaffer [6] considered a generalization of the standard p string matching, namely, dictionary matching under the parameterized pattern matching model. They used a modified Aho Corasick automaton [1] that, again, has a log(j Sigmaj j Pij) multiplicative factor. In this paper, we investigate the alphabet dependence in the complexity of the standard p string matching problem. We provide an algorithm for p string matching that takes time O(n log ) where = min(m; j Pij) independent of ....

....P 00 m matches T 00 at i. Similarly, it can be easily argued that if i 2 S 3 , then P p matches T beginning at i. We modify the KMP algorithm to solve the m matching problem simply by replacing every equality comparison x = y by x = y . Implementation of x = y Construct table A[1]; A[m] where A[i] the largest k; 1 k i, such that p k = p i . If no such k exists then A[i] i. The following subroutines compute p i = t j for j i, and p i = p j for j i. Compare(p i ,t j ) if A[i] i and t j 6= t j Gamma1 ; t j Gammai 1 then return ....

A.V. Aho and M.J. Corasick. Efficient string matching. Comm. ACM, 18(6):333--340, 1975.

....i.e. that of computing all the covers of a given n Theta n square matrix A. Fact 2. A cover of string x is also its border. A cover of matrix A is also its border. Proof . A cover of a string (matrix) occurs as both a prefix and a suffix and therefore it is a border. The Aho Corasick Automaton [AC75] was designed to solve the multi keyword pattern matching problem: given a set of keywords fr 1 ; r k g and an input string t, test whether or not a keyword r i occurs as a substring of t. The Aho Corasick pattern matching automaton is a six tuple (Q; Sigma; g; h; q 0 ; F ) where Q is a ....

.... is a six tuple (Q; Sigma; g; h; q 0 ; F ) where Q is a finite set of states, Sigma is a finite alphabet input, g : Q Theta Sigma Q [ fail is the forward transition, h : Q Q is the failure function (link) q 0 is the initial state and F is the set of final states (for details see [AC75]) Informally, the automaton can be represented as a rooted labeled tree augmented with the failure links. The label (denoted l s ) of the path from the root (initial state) to a state s is a prefix of one of the given keywords ; we denote such label by l s . If s is a final state , then l s is a ....

A.V.Aho and M.J.Corasick, Efficient string matching, Comm. ACM, Vol 18, No 6, 333-340, 1975

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A.V. Aho and M.J. Corasick [1975]. "Efficient string matching", C. ACM, 18:6, 333--340.

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