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A suffix can be seen as a special case of a substring. Example: The string nana is equal to a suffix (and substring and subsequence) of the string banana: banana |||| nana A suffix tree for a string is a trie data structure that represents all of its suffixes. Suffix trees have large numbers of applications in string algorithms.
In a complete suffix tree, all internal non-root nodes have a suffix link to another internal node. If the path from the root to a node spells the string χ α {\displaystyle \chi \alpha } , where χ {\displaystyle \chi } is a single character and α {\displaystyle \alpha } is a string (possibly empty), it has a suffix link to the internal node ...
Building the suffix tree takes () time (if the size of the alphabet is constant). If the tree is traversed from the bottom up with a bit vector telling which strings are seen below each node, the k-common substring problem can be solved in Θ ( N K ) {\displaystyle \Theta (NK)} time.
Let be the suffix array of the string =,, … $ of length , where $ is a sentinel letter that is unique and lexicographically smaller than any other character. Let [,] denote the substring of ranging from to .
Unique means that the substring occurs only once in each sequence. Finally, maximal states that the substring is not part of another larger string that fulfills both prior requirements. The idea behind this is that long sequences that match exactly and occur only once in each genome are almost certainly part of the global alignment.
By its definition, a suffix automaton can be obtained via minimization of the suffix trie. It may be shown that a compacted suffix automaton is obtained by both minimization of the suffix tree (if one assumes each string on the edge of the suffix tree is a solid character from the alphabet) and compaction of the suffix automaton. [17]
In computer science, the longest repeated substring problem is the problem of finding the longest substring of a string that occurs at least twice. This problem can be solved in linear time and space Θ ( n ) {\displaystyle \Theta (n)} by building a suffix tree for the string (with a special end-of-string symbol like '$' appended), and finding ...
You can find the following characteristics in a suffix tree that uses Ukkonen's algorithm: Implicit suffix tree T i+1 is built on top of implicit suffix tree T i. At any given time, Ukkonen's algorithm builds the suffix tree for the characters seen so far and so it has on-line property, allowing the algorithm to have an execution time of O(n).