Generalized suffix tree explained

In computer science, a generalized suffix tree is a suffix tree for a set of strings. Given the set of strings

D = S _{1,S} _{2,...,S} _{d} of total length n , it is a Patricia tree containing all n suffixes of the strings. It is mostly used in bioinformatics.

Functionality

It can be built in

\Theta(n) time and space, and can be used to find all z occurrences of a string P of length m in O(m + z) time, which is asymptotically optimal (assuming the size of the alphabet is constant).

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.

Algorithms for constructing a GST include Ukkonen's algorithm (1995) and McCreight's algorithm (1976).

Example

A suffix tree for the strings ABAB and BABA is shown in a figure above. They are padded with the unique terminator strings $0 and $1. 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 $ from the root are left out in this example.

Alternatives

An alternative to building a generalized 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.

References

^{[1] [2]}

External links

• • A C implementation of Generalized Suffix Tree for two strings

Notes and References

1. Paul Bieganski . John Riedl . John Carlis . Ernest F. Retzel . Generalized Suffix Trees for Biological Sequence Data . Biotechnology Computing, Proceedings of the Twenty-Seventh Hawaii International Conference on. . 1994 . 35 - 44 . 10.1109/HICSS.1994.323593 .
2. Book: Gusfield , Dan . 1997 . 1999 . Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology . Cambridge University Press . USA . 978-0-521-58519-4.