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It stores the lengths of the longest common prefixes (LCPs) between all pairs of consecutive suffixes in a sorted suffix array. For example, if A := [ aab , ab , abaab , b , baab ] is a suffix array, the longest common prefix between A [1] = aab and A [2] = ab is a which has length 1, so H [2] = 1 in the LCP array H .
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 ...
The final result is that the last cell contains all the longest subsequences common to (AGCAT) and (GAC); these are (AC), (GC), and (GA). The table also shows the longest common subsequences for every possible pair of prefixes. For example, for (AGC) and (GA), the longest common subsequence are (A) and (G).
See for example the suffix link from the node for ANA to the node for NA in the figure above. Suffix links are also used in some algorithms running on the tree. A generalized suffix tree is a suffix tree made for a set of strings instead of a single string. It represents all suffixes from this set of strings.
First, prefixes and suffixes, most of which are derived from ancient Greek or classical Latin, have a droppable vowel, usually -o-. As a general rule, this vowel almost always acts as a joint-stem to connect two consonantal roots (e.g. arthr- + -o- + -logy = arthrology ), but generally, the -o- is dropped when connecting to a vowel-stem (e.g ...
In the array, each suffix is represented by an integer pair (,) which denotes the suffix starting from position in . In the case where different strings in have identical suffixes, in the generalized suffix array, those suffixes will occupy consecutive positions. However, for convenience, the exception can be made where repeats will not be listed.
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.
Range minimum query reduced to the lowest common ancestor problem. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l … r].