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Concept
Suffix tree
Summary
In computer science, a suffix tree (also called PAT tree or, in an earlier form, position tree) is a compressed trie containing all the suffixes of the given text as their keys and positions in the text as their values. Suffix trees allow particularly fast implementations of many important string operations.
The construction of such a tree for the string takes time and space linear in the length of . Once constructed, several operations can be performed quickly, for instance locating a substring in , locating a substring if a certain number of mistakes are allowed, locating matches for a regular expression pattern etc. Suffix trees also provided one of the first linear-time solutions for the longest common substring problem. These speedups come at a cost: storing a string's suffix tree typically requires significantly more space than storing the string itself.
The concept was first introduced by .
Rather than the suffix , Weiner stored in his trie the prefix identifier for each position, that is, the shortest string starting at and occurring only once in . His Algorithm D takes an uncompressed trie for and extends it into a trie for . This way, starting from the trivial trie for , a trie for can be built by successive calls to Algorithm D; however, the overall run time is . Weiner's Algorithm B maintains several auxiliary data structures, to achieve an over all run time linear in the size of the constructed trie. The latter can still be nodes, e.g. for Weiner's Algorithm C finally uses compressed tries to achieve linear overall storage size and run time.
Donald Knuth subsequently characterized the latter as "Algorithm of the Year 1973".
The text book reproduced Weiner's results in a simplified and more elegant form, introducing the term position tree.
was the first to build a (compressed) trie of all suffixes of . Although the suffix starting at is usually longer than the prefix identifier, their path representations in a compressed trie do not differ in size.
Official source
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