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 {\displaystyle D=S_{1},S_{2},\dots ,S_{d}} of total length n {\displaystyle n} , it is a Patricia tree containing all n {\displaystyle n} suffixes of the strings. It is mostly used in bioinformatics.
Functionality It can be built in Θ ( n ) {\displaystyle \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 ) {\displaystyle 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
External links Media related to Generalized suffix tree at Wikimedia Commons A C implementation of Generalized Suffix Tree for two strings