Search results
Results from the WOW.Com Content Network
Given the suffix array and the LCP array of a string =,, … $ of length +, its suffix tree can be constructed in () time based on the following idea: Start with the partial suffix tree for the lexicographically smallest suffix and repeatedly insert the other suffixes in the order given by the suffix array.
Then, sorting a subset of is equivalent to convert it into an increasing sequence. The lexicographic order on the resulting sequences induces thus an order on the subsets, which is also called the lexicographical order. In this context, one generally prefer to sort first the subsets by cardinality, such as in the shortlex order. Therefore, in ...
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.
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}} .
One implementation can be described as arranging the data sequence in a two-dimensional array and then sorting the columns of the array using insertion sort. The worst-case time complexity of Shellsort is an open problem and depends on the gap sequence used, with known complexities ranging from O ( n 2 ) to O ( n 4/3 ) and Θ( n log 2 n ).
According to the Chen–Fox–Lyndon theorem, every string may be formed in a unique way by concatenating a sequence of Lyndon words, in such a way that the words in the sequence are nonincreasing lexicographically. [8] The final Lyndon word in this sequence is the lexicographically smallest suffix of the given string. [9]
More generally objects can be sorted based on a property. Such a component or property is called a sort key. For example, the items are books, the sort key is the title, subject or author, and the order is alphabetical. A new sort key can be created from two or more sort keys by lexicographical order.
Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. [citation needed]Elements within a sorted array are found using a binary search, in O(log n); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure.