Apostolico–Giancarlo algorithm: Difference between revisions

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{{shortShort description|Optimization of Boyer–Moore string -search algorithm}}

{{No footnotes|date=October 2023}}

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 <math>{{mvar|P</math>}} in a text <math>{{mvar|T</math>}}. As with other comparison-based string searches, this is done by aligning <math>{{mvar|P</math>}} to a certain index of <math>{{mvar|T</math>}} and checking whether a match occurs at that index. <math>{{mvar|P</math>}} is then shifted relative to <math>{{mvar|T</math>}} according to the rules of the Boyer–Moore algorithm, and the process repeats until the end of <math>{{mvar|T</math>}} has been reached. Application of the Boyer-MooreBoyer–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-MooreBoyer–Moore, finding an occurrence of <math>{{mvar|P</math>}} in <math>{{mvar|T</math>}} requires that all <math>{{mvar|n</math>}} characters of <math>{{mvar|P</math>}} 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 <{{math>|O(n m''nm'')</math>}}, where <math>{{mvar|m</math>}} is the length in characters of <math>{{mvar|T</math>}}. Apostolico–Giancarlo speeds this up by recording the number of characters matched at the alignments of <math>{{mvar|T</math>}} in a table, which is combined with data gathered during the pre-processing of <math>{{mvar|P</math>}} to avoid redundant equality checking for sequences of characters that are known to match. It can be seen as a generalization of the [[Galil rule]].

==References==

* {{cite journal |doi=10.1137/0215007 |title=The Boyer–Moore–Galil String Searching Strategies Revisited |year=1986 |last1=Apostolico |first1=Alberto |last2=Giancarlo |first2=Raffaele |journal=[[SIAM Journal on Computing]] |volume=15 |pages=98–105 |url=https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1456&context=cstech}}

* {{cite journal |doi=10.1016/S0020-0190(97)00107-5 |title=Tight bounds on the complexity of the Apostolico-Giancarlo algorithm |year=1997 |last1=Crochemore |first1=Maxime |last2=Lecroq |first2=Thierry |journal=[[Information Processing Letters]] |volume=63 |issue=4 |pages=195–203 |url=https://hal-upec-upem.archives-ouvertes.fr/hal-00619574/file/ipl2.pdf}}

* {{cite book |last=Crochemore |lastfirst1=M. |last2=Rytter |first2=W. |author2-link=Wojciech Rytter |year=1994 |title=Text Algorithms |publisher=[[Oxford University Press]]}}

* {{cite book |last=Gusfield |first=D. |year=1997 |title=Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology |publisher=[[Cambridge University Press]] |isbn=0-521-58519-8}}

* {{cite thesis |last=Lecroq |first=T. |year=1992 |title=Recherches de Mots |type=Ph. D. Thesis |publisher=[[University of Orléans]]}}