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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 ...
For example, the longest palindromic substring of "bananas" is "anana". The longest palindromic substring is not guaranteed to be unique; for example, in the string "abracadabra", there is no palindromic substring with length greater than three, but there are two palindromic substrings with length three, namely, "aca" and "ada".
A string is a substring (or factor) [1] of a string if there exists two strings and such that =.In particular, the empty string is a substring of every string. Example: The string = ana is equal to substrings (and subsequences) of = banana at two different offsets:
Black dots represent candidates that would have to be considered by the simple algorithm and the black lines are connections that create common subsequences of length 3. Red dots represent k-candidates that are considered by the Hunt–Szymanski algorithm and the red line is the connection that creates a common subsequence of length 3.
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]
Comparison of two revisions of an example file, based on their longest common subsequence (black) A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences).
The closely related problem of finding a minimum-length string which is a superstring of a finite set of strings S = { s 1,s 2,...,s n} is also NP-hard. [2] Several constant factor approximations have been proposed throughout the years, and the current best known algorithm has an approximation factor of 2.475. [3]
It is a simplification of the Boyer–Moore string-search algorithm which is related to the Knuth–Morris–Pratt algorithm. The algorithm trades space for time in order to obtain an average-case complexity of O(n) on random text, although it has O(nm) in the worst case, where the length of the pattern is m and the length of the search string ...