The Boyer Moore Galil string searching strategies revisited
SIAM Journal on Computing
Average running time of the Boyer-Moore-Horspool algorithm
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
Autocorrelation on words and its applications: analysis of suffix trees by string-ruler approach
Journal of Combinatorial Theory Series A
Text algorithms
Tighter Lower Bounds on the Exact Complexity of String Matching
SIAM Journal on Computing
Analysis of Boyer-Moore-Horspool string-matching heuristic
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
A fast string searching algorithm
Communications of the ACM
Knuth-Morris-Pratt Algorithm: An Analysis
MFCS '89 Proceedings on Mathematical Foundations of Computer Science 1989
Tight Comparison Bounds for the String Prefix-Matching Problem
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
On the exact complexity of string matching
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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We formally define a class of sequential pattern matching algorithms that includes all variations of Morris-Pratt algorithm. For the last twenty years it was known that the complexity of such algorithms is bounded by a linear function of the text length. Recently, substantial progress has been made in identifying lower bounds. We now prove there exists asymptotically a linearity constant for the worst and the average cases. We use Subadditive Ergodic Theorem and prove an almost sure convergence. Our results hold for any given pattern and text and for stationary ergodic pattern and text. In the course of the proof, we establish some structural property, namely, the existence of "unavoidable positions" where the algorithm must stop to compare. This property seems to be uniquely reserved for Morris-Pratt type algorithms (e.g., Boyer and Moore algorithm does not possess this property).