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| [[Image:Suffix tree ABAB BABA.svg|thumb|300px|right|Suffix tree for the strings <code>ABAB</code> and <code>BABA</code>. [[Suffix_tree#Description|Suffix links]] not shown.]]
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| In [[computer science]], a '''generalized suffix tree''' is a [[suffix tree]] for a set of [[String (computer science)|strings]]. Given the set of strings <math>D=S_1,S_2,\dots,S_d</math> of total length <math>n</math>, it is a [[Patricia tree]] containing all <math>n</math> [[suffix (computer science)|suffixes]] of the strings. It is mostly used in [[bioinformatics]].{{ref|BRCR}}
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| == Functionality ==
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| It can be built in <math>\Theta(n)</math> time and space, and can be used to find all <math>z</math> occurrences of a string <math>P</math> of length <math>m</math> in <math>O(m + z)</math> time, which is [[asymptotically optimal]] (assuming the size of the alphabet is constant, see {{ref|Gus97}} page 119).
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| When constructing such a tree, each string should be padded with a unique out-of-alphabet marker symbol (or string) to ensure no suffix is a substring of another, guaranteeing each suffix is represented by a unique leaf node.
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| Algorithms for constructing a GST include [[Ukkonen's algorithm]] (1995) and [[McCreight's algorithm]] (1976).
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| == Example ==
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| A suffix tree for the strings <code>ABAB</code> and <code>BABA</code> is shown in a figure above. They are padded with the unique terminator strings <code>$0</code> and <code>$1</code>. The numbers in the leaf nodes are string number and starting position. Notice how a left to right traversal of the leaf nodes corresponds to the sorted order of the suffixes. The terminators might be strings or unique single symbols. Edges on <code>$</code> from the root are left out in this example.
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| == Alternatives ==
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| An alternative to building a generalised suffix tree is to concatenate the strings, and build a regular suffix tree or [[suffix array]] for the resulting string. When hits are evaluated after a search, global positions are mapped into documents and local positions with some algorithm and/or data structure, such as a binary search in the starting/ending positions of the documents.
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| ==References==
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| * {{note|Hui92}} {{cite conference
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| | author=Lucas Chi Kwong Hui
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| | title=Color Set Size Problem with Applications to String Matching
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| | booktitle=Combinatorial Pattern Matching, Lecture Notes in Computer Science, 644.
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| | year=1992
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| | pages=230–243
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| | url=http://www.springerlink.com/content/y565487707522555/}}
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| * {{note|BRCR}} {{cite conference
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| | author=Paul Bieganski, John Riedl, John Carlis, and Ernest F. Retzel
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| | title=Generalized Suffix Trees for Biological Sequence Data
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| | booktitle=Biotechnology Computing, Proceedings of the Twenty-Seventh Hawaii International Conference on.
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| | year=1994
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| | pages=35–44
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| | url=http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=323593}}
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| * {{note|Gus97}} {{cite book
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| | last = Gusfield
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| | first = Dan
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| | origyear = 1997
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| | year = 1999
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| | title = Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology
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| | publisher = Cambridge University Press
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| | location = USA
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| | isbn = 0-521-58519-8
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| }}
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| [[Category:Trees (data structures)]]
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| [[Category:Substring indices]]
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| [[Category:String data structures]]
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The writer is called Wilber Pegues. What I love performing is football but I don't have the time recently. My working day job is an invoicing officer but I've currently applied for another 1. My spouse and I live in Mississippi and I love each day residing here.
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