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  2. Lexicographic order - Wikipedia

    en.wikipedia.org/wiki/Lexicographic_order

    In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering.

  3. Burrows–Wheeler transform - Wikipedia

    en.wikipedia.org/wiki/Burrows–Wheeler_transform

    The Burrows–Wheeler transform (BWT, also called block-sorting compression) rearranges a character string into runs of similar characters. This is useful for compression, since it tends to be easy to compress a string that has runs of repeated characters by techniques such as move-to-front transform and run-length encoding.

  4. Suffix array - Wikipedia

    en.wikipedia.org/wiki/Suffix_array

    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.

  5. Shortlex order - Wikipedia

    en.wikipedia.org/wiki/Shortlex_order

    In mathematics, and particularly in the theory of formal languages, shortlex is a total ordering for finite sequences of objects that can themselves be totally ordered. In the shortlex ordering, sequences are primarily sorted by cardinality (length) with the shortest sequences first, and sequences of the same length are sorted into lexicographical order. [1]

  6. Generalized suffix array - Wikipedia

    en.wikipedia.org/wiki/Generalized_suffix_array

    It is a lexicographically sorted array of all suffixes of each string in the set . In the array, each suffix is represented by an integer pair ( i , j ) {\displaystyle (i,j)} which denotes the suffix starting from position j {\displaystyle j} in s i {\displaystyle s_{i}} .

  7. Trie - Wikipedia

    en.wikipedia.org/wiki/Trie

    Lexicographic sorting of a set of string keys can be implemented by building a trie for the given keys and traversing the tree in pre-order fashion; [26] this is also a form of radix sort. [27] Tries are also fundamental data structures for burstsort , which is notable for being the fastest string sorting algorithm as of 2007, [ 28 ...

  8. Path ordering (term rewriting) - Wikipedia

    en.wikipedia.org/wiki/Path_ordering_(term_rewriting)

    There may also be systems for certain general recursive functions, for example a system for the Ackermann function may contain the rule A(a +, b +) → A(a, A(a +, b)), [1] where b + denotes the successor of b. Given two terms s and t, with a root symbol f and g, respectively, to decide their relation their root symbols are compared first.

  9. LCP array - Wikipedia

    en.wikipedia.org/wiki/LCP_array

    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 .