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A naive implementation would compute the largest common subsequence of all the strings in the set in (). [ 6 ] A generalized suffix array can be utilized to find the longest previous factor array, a concept central to text compression techniques and in the detection of motifs and repeats [ 7 ]
The string spelled by the edges from the root to such a node is a longest repeated substring. The problem of finding the longest substring with at least k {\displaystyle k} occurrences can be solved by first preprocessing the tree to count the number of leaf descendants for each internal node, and then finding the deepest node with at least k ...
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...
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 ...
[1] [2] These data structures enable quick search for an arbitrary string with a comparatively small index. Given a text T of n characters from an alphabet Σ, a compressed suffix array supports searching for arbitrary patterns in T. For an input pattern P of m characters, the search time is typically O(m) or O(m + log(n)).
The suffix tree for the string of length is defined as a tree such that: [7]. The tree has exactly n leaves numbered from to .; Except for the root, every internal node has at least two children.
Suffix arrays are closely related to suffix trees: . Suffix arrays can be constructed by performing a depth-first traversal of a suffix tree. The suffix array corresponds to the leaf-labels given in the order in which these are visited during the traversal, if edges are visited in the lexicographical order of their first character.
Ukkonen's algorithm is divided into n phases (one phase for each character in the string with length n). Each phase i+1 is further divided into i+1 extensions, one for each of the i+1 suffixes of S[1...i+1]. Suffix extension is all about adding the next character into the suffix tree built so far.