Amir, A., Farach, M., and Muthukrishnan, S. Alphabet dependence in parameterized matching. Information Processing Letters 49, 3 (1994), 111--115.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....2 matches starting at positions 7 and 12. However if we require that the naming function is injective then we have only one match. In what follows we consider only noninjective naming functions. The injective case has been studied extensively in the context of parameterized string matching, see [1, 4 6]. a e c d a b a a d b d d a b a a c a c c b a a b b d b a c d b a . a . d . equal equal interpretation of the pattern xayzdyx occurrences x a y z d y x x a y z d y x Fig. 2. There are exactly two occurrences of the pattern xayzdyx with variables x; y; z whose possible values are single ....

A. Amir, M. Farach, and S. Muthukrishnan, Alphabet dependence in parameterized matching, Information Processing Letters (49)3 (1994) pp. 111-115.

.... Boyer Moore algorithms for parameterized pattern matching [Baker93c] Amir et al. have also generalized the Knuth Morris Pratt algorithm to find p matches in O(nlog(min(m , P ) time, where n is text length and m is pattern length, and have shown that this is optimal under a comparison model [AFM93]. For p matching a set of p string patterns, Idury and Schaffer [ID93] have developed generalizations of the AhoCorasick algorithm [AC75] for matching multiple patterns and of their dynamic dictionary algorithm for strings [ID92] Let tocc be the number of occurrences found, and d be the sum of ....

Amihood Amir, Martin Farach, and S. Muthukrishnan, Alphabet dependence in parameterized matching, submitted for publication, 1993.

....program fragments are represented by some parameterized strings, called p strings. A suffix tree generalization, called p suffix tree [7] allows us to search for p strings online and to identify p string duplications by ignoring parameter renaming. P suffix trees and the other p string algorithms [4, 26, 30] are designed to work in main memory and have to deal with the dynamic nature of parameter renaming. We can formulate Problems 1 and 2 for p strings and then apply String B trees to them by means of some minor algorithmic modifications. Consequently, the aforementioned theoretical results ....

....give an example of PT Search(P , S ) in Figure 6, where P = bcbabcba . In particular, Figure 6(left) depicts the first phase in which l represents the rightmost leaf. It is worth noting that l does not identify P s position in S because we do not compare P s mismatching character (i.e. P [4] = a ) and thus we induce a mistake. We determine P s correct position in the second phase, illustrated in Figure 6(right) We start out by determining the common prefix of l s string and P (i.e. bcb ) and then we find l s shallowest ancestor (the hit node) whose label is greater than ....

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Amir, A., Farach, M., and Muthukrishnan, S. Alphabet dependence in parameterized matching. Information Processing Letters 49 (1994), 111--115.

.... We derive a generalization to p strings that we call the PturboBM algorithm, and show that under a comparison model it runs in time O(n log min(m; p) and space O(n) with preprocessing time O(m log min(m; p) These bounds are the same as for a generalization of the KMP algorithm to p strings [AFM94, IS94] and are optimal [AFM94] However, in experiments, for sufficiently long patterns and a variety of choices of alphabet sizes, an implementation of PturboBM performed better than a generalization of the KMP algorithm on random input under a uniform distribution. Careful experiments on input ....

.... p strings that we call the PturboBM algorithm, and show that under a comparison model it runs in time O(n log min(m; p) and space O(n) with preprocessing time O(m log min(m; p) These bounds are the same as for a generalization of the KMP algorithm to p strings [AFM94, IS94] and are optimal [AFM94] However, in experiments, for sufficiently long patterns and a variety of choices of alphabet sizes, an implementation of PturboBM performed better than a generalization of the KMP algorithm on random input under a uniform distribution. Careful experiments on input obtained from software have ....

Amihood Amir, Martin Farach, and S. Muthukrishnan. Alphabet dependence in parameterized matching. Info. Proc. Letters, 49:111--115, 1994.

....nition 2 The subsequence character count problem is de ned as follows: INPUT: Array S = s 1 ; s n of symbols over alphabet and a natural number m. OUTPUT: For every i; i = 1; n m 1; the number of di erent alphabet symbols occurring in the subsequence s i ; s i 1 ; s i m 1 . In [4] the problem was used to solve the parameterized matching problem. The sliding window technique keeps a list of counters of the number of occurrences of every symbol in the window, and a variable D designating the number of di erent symbols in the window. When sliding from position i to position ....

A. Amir, M. Farach, and S. Muthukrishnan. Alphabet dependence in parameterized matching. Information Processing Letters, 49:111-115, 1994.

....pattern but the matching relation is defined differently. The output is all locations in the text where the pattern matches under the new definition of match. The different applications define the matching relation. Examples are string matching with don t cares [12] parameterized matching [8, 4], less than matching [3] and swapped matching [21, 2, 9] Lower bound results on generalized matching can be found in [22] Even under the appropriate matching relation there is still a distinction between exact matching and approximate matching. In the latter case, a distance function is ....

A. Amir, M. Farach, and S. Muthukrishnan. Alphabet dependence in parameterized matching. Information Processing Letters, 49:111--115, 1994.

....and pattern but the matching relation is defined di#erently. The output is all locations in the text where the pattern matches under the new definition of match. The di#erent applications define the matching relation. Examples are string matching with don t cares [12] parameterized matching [8, 4], less than matching [3] and swapped matching [21, 2, 9] Lower bound results on generalized matching can be found in [22] Even under the appropriate matching relation there is still a distinction between exact matching and approximate matching. In the latter case, a distance function is ....

A. Amir, M. Farach, and S. Muthukrishnan. Alphabet dependence in parameterized matching. Information Processing Letters, 49:111--115, 1994.

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Amir, A., Farach, M., and Muthukrishnan, S. Alphabet dependence in parameterized matching. Information Processing Letters 49, 3 (1994), 111--115.

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