The Boyer-Moore-Horspool heuristic with Markovian input

Abstract

The Boyer–Moore–Horspool string-matching heuristic is an algorithm for locating occurrences of a fixed pattern in a random text. Under the assumption that the text is an independently and identically distributed sequence of characters, the probabilistic behavior of this algorithm was investigated by Mahmoud, Smythe, and Régnier [Random Struct Alg 10 (1997), 169–186]. Here, we obtain similar results under the assumption that the text is generated by an irreducible Markov chain. A natural Markov renewal process structure is exploited to obtain the asymptotic behavior of the number of comparisons. Under suitable normalization, it is shown that a central limit theorem holds for the number of comparisons. The analysis is completely probabilistic and does not use the shift generating function. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 153–163, 2001