Analysis of Boyer-Moore-Horspool string-matching heuristic

Abstract

We investigate the probabilistic behavior of a string-matching heuristic used for searching for the occurrences of a pattern in a random text. Our investigation covers the two cases when the pattern itself is fixed or random. Under suitable normalization we show that the total search time is asymptotically normally distributed in the case of fixed pattern, whereas in the case of random pattern the distribution of the search time becomes a mixture of degenerate distributions. An instrumental recurrence equation is obtained by shifting the pattern within the text. To handle the sum of dependent random variables appearing in the recurrence, analytic methods based on the behavior of the shift generating function near its dominant singularity in the complex plane are devised to yield moment calculation and the asymptotic distributions. Adaptation of the standard central limit theorem under mixing conditions complements our analytic toolkit. P P P characterized by J, and we shall simply use the notation , c , r for all patterns J J J Ž . sharing the same J. The sums below are taken over every multiset J satisfying 1 . Ý Ł m m J r ž / J js2 J

Performance Analysis of Machine Learning and Pattern Matching Techniques for Deep Packet Inspection in Firewalls

“…The inputs to the Algorithm are pattern (signature) and text (data) from the pattern to be searched, meanwhile the output is a Boolean value. The Boyer-Moore-Horspool (BMHP) algorithm [18] is shown in Algorithm 1.…”

“…The BHMP is faster, simpler and optimized for searching the sub strings such that worst-case the performance of the BHMP algorithm is O(mn). Here, 'm' signifies the length of the pattern and 'n' denotes the length of the text [17], [18].…”

Similarity Detection for Hadith of Fiqh of Women using Cosine Similarity and Boyer Moore Method

“…The following will be illustrated an example of its application to better understand the search system using the Boyer-Moore algorithm in the application to be made, using the word you want to find (pattern) "HAID" in the text "OLD HAID" [21], [22].…”

“…The first step in matching this string is finding the values for BMBC and BMGS [14], [21], [23]. The value of the results of this preprocessing calculation will be displayed in Table 1.…”

Designing optimal- and fast-on-average pattern matching algorithms

“…Asymptotic speeds for some patterns of length 10 on {a, b} (drawn from the uniform distribution) under the iid model (π a , π b ) = (0.1, 0.9). .76 1.60 1.45 0.67 3.01 3 16. 3.16 3.11 3.01 3.16 3.16 3.16 at d 3.15 2.02 1.85 1.46 0.66 2.96 3.22 3.22 3.22 2.96 3.22 3.22 3.22 f th 2.72 1.81 1.69 1.35 0.65 2.94 3.03 2.87 3.05 2.94 3.10 3.10 3.10 r th 2.73 1.80 1.69 1.36 0.66 2.94 3.04 2.87 3.06 2.94 3.12 3.12 3.12 fede 3.35 1.97 1.73 1.49 0.66 3.23 3.53 3.53 3.53 3.23 3.53 3.53 3.53…”