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In computer science, a suffix array is a sorted array of all suffixes of a string. It is a data structure used in, among others, full-text indices, data-compression algorithms, and the field of bibliometrics. Suffix arrays were introduced by Manber & Myers (1990) as a simple, space efficient alternative to suffix trees.
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.
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.
This ensures that no suffix is a prefix of another, and that there will be leaf nodes, one for each of the suffixes of . [8] Since all internal non-root nodes are branching, there can be at most n − 1 {\displaystyle n-1} such nodes, and n + ( n − 1 ) + 1 = 2 n {\displaystyle n+(n-1)+1=2n} nodes in total ( n {\displaystyle n} leaves, n − 1 ...
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. The suffix array is a simplified version of this data structure that lists the start positions of the suffixes in alphabetically sorted order; it has many of the same applications.
Meaning Origin language and etymology Example(s) -iasis: condition, formation, or presence of Latin -iasis, pathological condition or process; from Greek ἴασις (íasis), cure, repair, mend mydriasis: iatr(o)-of or pertaining to medicine or a physician (uncommon as a prefix but common as a suffix; see -iatry)
Adding a prefix to the beginning of an English word changes it to a different word. For example, when the prefix un-is added to the word happy, it creates the word unhappy. The word prefix is itself made up of the stem fix (meaning "attach", in this case), and the prefix pre-(meaning "before"), both of which are derived from Latin roots.
As with a prefix code, the representation of a string as a concatenation of such words is unique. A bifix code is a set of words which is both a prefix and a suffix code. [8] An optimal prefix code is a prefix code with minimal average length. That is, assume an alphabet of n symbols with probabilities () for a prefix code C.