List of convolutions of probability distributions

In computer science, the Apostolico–Giancarlo algorithm is a variant of the Boyer-Moore string search algorithm, the basic application of which is searching for occurrences of a pattern $P$ in a text $T$. As with other comparison-based string searches, this is done by aligning $P$ to a certain index of $T$ and checking whether a match occurs at that index. $P$ is then shifted relative to $T$ according to the rules of the Boyer-Moore algorithm, and the process repeats until the end of $T$ has been reached. Application of the Boyer-Moore shift rules often results in large chunks of the text being skipped entirely.

With regard to the shift operation, Apostolico-Giancarlo is exactly equivalent in functionality to Boyer-Moore. The utility of Apostolico-Giancarlo is to speed up the match-checking operation at any index. With Boyer-Moore, finding an occurrence of $P$ in $T$ requires that all $n$ characters of $P$ be explicitly matched. For certain patterns and texts, this is very inefficient - a simple example is when both pattern and text consist of the same repeated character, in which case Boyer-Moore runs in $O(nm)$ where $m$ is the length in characters of $T$. Apostolico-Giancarlo speeds this up by recording the number of characters matched at the alignments of $T$ in a table, which is combined with data gathered during the pre-processing of $P$ to avoid redundant equality checking for sequences of characters that are known to match.

References

• Apostolico A., Giancarlo R., 1986, The Boyer-Moore-Galil string searching strategies revisited, SIAM Journal on Computing 15(1):98-105.
• Crochemore, M., Lecroq, T., 1997, Tight bounds on the complexity of the Apostolico–Giancarlo algorithm, Information Processing Letters 63(4):195-203.
• Crochemore, M., Rytter, W., 1994, Text Algorithms, Oxford University Press.
• Gusfield, D., 1997, Algorithms on strings, trees, and sequences: Computer Science and Computational Biology, Cambridge University Press.
• Lecroq, T., 1992, Recherches de mot, Ph. D. Thesis, University of Orléans, France.
• Lecroq, T., 1995, Experimental results on string matching algorithms, Software - Practice & Experience 25(7):727-765.