Showing papers by "Richard Cole published in 1994"
TL;DR: The Boyer--Moore string matching algorithm performs roughly $3n$ comparisons and this bound is tight up to $O(n/m)$; more precisely, an upper bound of 3n - 3(n-m+1)/(m+2)$ comparisons is shown, as is a lower bound of $3 n(1-o(1))$ comparisons.
Abstract: The problem of finding all occurrences of a pattern of length $m$ in a text of length $n$ is considered. It is shown that the Boyer--Moore string matching algorithm performs roughly $3n$ comparisons and that this bound is tight up to $O(n/m)$; more precisely, an upper bound of $3n - 3(n-m+1)/(m+2)$ comparisons is shown, as is a lower bound of $3n(1-o(1))$ comparisons, as $\frac{n}{m}\rightarrow\infty$ and $m\rightarrow\infty$. While the upper bound is somewhat involved, its main elements provide a simple proof of a $4n$ upper bound for the same algorithm.
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