L. Colussi, Z. Galil, and R. Giancarlo. On the exact complexity of string matching. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 135--144, Baltimore, MD, May 14--16, 1990. ACM Press, New York, NY.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....compare = 1) characters before two strings mismatch. Our aim is to do better. From a theoretical viewpoint, this problem is basically solved, except for very focused questions that still remain. The worst case complexity is clearly n) character inspections (for the exact constant see [18]) This has been achieved by Knuth Morris Pratt (KMP) algorithm [41] using O(m) space. The average case complexity is n log (m) m) 76] This has been achieved by Backward DAWG Matching (BDM) algorithm [21] using O(m) space. The algorithm can be made worst case optimal at the same time ....

L. Colussi, Z. Galil, and R. Giancarlo. The exact complexity of string matching. In Proc. 31st IEEE Ann. Symp. on Foundations of Computer Science, volume 1, pages 135-143, 1990.

....Apostolico and Giancarlo [AG86] gave a variant of the BM algorithm which makes at most 2n m 1 comparisons. Crochemore et al. CCG92] showed recently that remembering just the most recently matched portion reduces the upper bound of BM from 3n to 2n comparisons. Recently, Galil and Giancarlo [CGG90], GG92] analyzed and modi ed a string matching algorithm designed by Colussi [Coll91] they showed it makes at most n comparisons. In fact, GG92] give this bound in a sharper form as a function of the period z of the pattern; the bound becomes n (n m) minf ; minfz;m zg 2 g. Galil ....

L. Colussi, Z. Galil, R. Giancarlo, On the Exact Complexity of String Matching, Proceedings of the 31st Annual IEEE Symposium on the Foundations of Computer Science, (1990), pp. 135-143.

....number of occurrences of a searched pattern P in all possible texts, hence, to maximal coverings of the text by the pattern. As P can overlap with himself, these may not be tilings. This can be expressed as a function of a canonical decomposition of P . Let us say a few words on 1D complexity [8]. It is proved in [11] that a self overlapping pattern can be written p = u(vu) m ; m 1; u 6= ffl, where vu is primitive, i.e. not the power of any word w. The pattern p is periodic if and only if m 2. As discussed in [12] the decomposition is not unique although at most one satisfies m 2. ....

L. Colussi, Z. Galil, and R. Giancarlo. On the exact Complexity of string matching. In FOCS'90, pages 135--143. IEEE, 1990. Proc. 31-st Annual IEEE Symposium on the Foundations of Computer Science.

....[14] and these bounds are tight. The 2 n o(n) barrier was first beaten by Colussi et al. see [18] They designed a simple variant of KMP algorithm that performs at most 3 2 n comparisons. A similar result was obtained independently by Apostolico and Crochemore [5] Colussi, Galil and Giancarlo [19] gave an algorithm that makes at most n 1 3 (n m) comparisons in the search phase. This bound was improved later by Breslauer and Galil [13] who obtained a searching stage (followed by a linear time preprocessing phase) that uses n 4 log m 2 m (n m) comparisons in the worst case ....

L. Colussi, Z. Galil, and R. Giancarlo. On the exact complexity of string matching. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 135--144, Baltimore, MD, May 14--16, 1990. ACM Press, New York, NY.

....and Giancarlo [AG86] gave a variant of the BM algorithm which makes at most 2n Gamma m 1 comparisons. Crochemore et al. CCG92] showed recently that remembering just the most recently matched portion reduces the upper bound of BM from 3n to 2n comparisons. Recently, Galil and Giancarlo [CGG90], GG92] analyzed and modified a string matching algorithm designed by Colussi [Coll91] they showed it makes at most 4 3 n comparisons. In fact, GG92] give this bound in a sharper form as a function of the period z of the pattern; the bound becomes n (n Gamma m)minf 1 3 ; ....

L. Colussi, Z. Galil, R. Giancarlo, On the Exact Complexity of String Matching, Proceedings of the 31st Annual IEEE Symposium on the Foundations of Computer Science, (1990), pp. 135--143.

.... of comparisons of the Boyer Moore algorithm [Col91a] and several papers dealing with the average case analysis of this algorithm [BYGR90, Sch88] ffl the 4 3n upper bound in the worst case number of comparisons with a (1 1 (2m) n lower bound for any comparison based string matching algorithm [CGG90]; ffl some results concerning the maximal number of states of a Boyer Moore type automaton [BYR90, Cho90, Bru91] a problem that is still open; ffl improvement of several variations of approximate string matching [WMM91] ffl the derivation of classical and improved algorithms through formal ....

L. Colussi, Z. Galil, and R. Giancarlo. The exact complexity of string matching. In 31st FOCS, volume 1, pages 135--143, St. Louis, MO, Oct 1990. IEEE.

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L. Colussi, Z. Galil, R. Giancarlo. On the Exact Complexity of String Matching. Proceedings of the 31st Annual IEEE Symposium on the Foundations of Computer Science, 1990, pp. 135-143.

....on the exact complexity of the string matching problem. Namely, the exact number of comparisons necessary in the case of a general alphabet. Surprisingly, the upper bound of about 2n comparisons, the best known before [5, 35] was improved to 4 3 n comparisons by Colussi, Galil and Giancarlo [16]. In a recent work Cole [17] proved that the number of comparisons performed by the original Boyer Moore algorithm is about 3n. In this paper we will focus on parallel algorithms for the string matching problem. Many other related problems have been investigated and are out of the scope of this ....

Colussi, L., Galil, Z. and Giancarlo, R. (1990), On the exact complexity of string matching, Proc. 31st IEEE Symp. on Foundations of Computer Science, 135-143.

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L. Colussi, Z. Galil, and R. Giancarlo. On the exact complexity of string matching. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 135--144, Baltimore, MD, May 14--16, 1990. ACM Press, New York, NY.

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L. Colussi, Z. Galil, R. Giancarlo. On the Exact Complexity of String Matching. Proceedings of the Thirty First Annual IEEE Symposium on the Foundations of Computer Science, 1990, 135--143.

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L. Colussi, Z. Galil, R. Giancarlo. On the Exact Complexity of String Matching. Proceedings of the Thirty First Annual IEEE Symposium on the Foundations of Computer Science, 1990, 135--143.

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L. Colussi, Z. Galil, R. Giancarlo. On the Exact Complexity of String Matching. Proceedings of the Thirty First Annual IEEE Symposium on the Foundations of Computer Science, 1990, 135--143.

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L. Colussi, Z. Galil, and R. Giancarlo, `The exact complexity of string matching,' 31st Symposium an Foun- dations of Computer Science I, 135--143, IEEE (October 22-24 1990).

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