Substring index: Difference between revisions

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{{Short description|Data structure}}

In [[computer science]], a '''substring index''' is a [[data structure]] which gives [[substring]] search in a text or text collection in [[sublinear]] time. IfOnce youconstructed havefrom a document <math>S</math> of length <math>n</math>, or a set of documents <math>D=\{S^1,S^2, \dots,a S^d\}</math>substring ofindex totalcan lengthbe <math>n</math>,used you canto locate all occurrences of a pattern <math>P</math>in time linear or near-linear in <math>o(n)</math>the time.pattern (Seesize, [[Bigwith Ono notation|Bigdependence ''O''or notation]]only logarithmic dependence on the document size.)<ref name=bst>{{citation

{{more references|date=December 2021}}

| last1 = Barsky | first1 = Marina

In [[computer science]], a '''substring index''' is a [[data structure]] which gives [[substring]] search in a text or text collection in [[sublinear]] time. If you have a document <math>S</math> of length <math>n</math>, or a set of documents <math>D=\{S^1,S^2, \dots, S^d\}</math> of total length <math>n</math>, you can locate all occurrences of a pattern <math>P</math> in <math>o(n)</math> time. (See [[Big O notation|Big ''O'' notation]].)

| last2 = Stege | first2 = Ulrike

| last3 = Thomo | first3 = Alex

| contribution = Chapter 1: Structures for Indexing Substrings

| doi = 10.1007/978-3-031-01885-5_1

| isbn = 9783031018855

| pages = 1–15

| publisher = Springer International Publishing

| series = Synthesis Lectures on Data Management

| title = Full-Text (Substring) Indexes in External Memory

| year = 2012}}</ref>

The phrase '''full-text index''' is also often used for an index of all substrings of asubstring textindexes. But this is ambiguous, as it is also used for regular word indexes such as [[inverted file]]s and [[document retrieval]]. See [[full text search]].

==General considerations==

Substring indexes include:

These data structures typically treat their text and pattern as [[string (computer science)|strings]] over a fixed alphabet, and search for locations where the pattern occurs as a substring of the text. The symbols of the alphabet may be characters (for instance in [[Unicode]]) but in practical applications for [[text retrieval]] it may be preferable to treat the ([[Stemming|stemmed]]) words of a document as the symbols of its alphabet, because doing this reduces the lengths of both the text and pattern as measured in numbers of symbols.<ref>{{citation

| last = Risvik | first = Knut Magne

| editor-last = Farach-Colton | editor-first = Martin | editor-link = Martin Farach-Colton

| contribution = Approximate word sequence matching over sparse suffix trees

| doi = 10.1007/BFB0030781

| pages = 65–79

| publisher = Springer

| series = Lecture Notes in Computer Science

| title = Combinatorial Pattern Matching, 9th Annual Symposium, CPM 98, Piscataway, New Jersey, USA, July 20–22, 1998, Proceedings

| volume = 1448

| year = 1998| isbn = 978-3-540-64739-3

}}</ref>

==Examples==

* [[Suffix tree]]

Specific data structures that can be used as substring indexes include:

* [[Suffix array]]

* The [[suffix tree]], a [[radix tree]] of the suffixes of the string, allowing substring search to be performed symbol-by-symbol<ref name=bst/><ref name=gv/>

* N-gram index, an [[inverted file]] for all [[N-gram]]s of the text

* The [[suffix automaton]], the minimal [[deterministic finite automaton]] that recognizes substrings of a given text, closely related to the suffix tree and constructable by variants of the same algorithms.<ref>{{citation

* [[Compressed suffix array]]<ref>R. Grossi and J. S. Vitter, [http://www.di.unipi.it/~grossi/PAPERS/sicomp05.pdf Compressed Suffix Arrays and Suffix Trees, with Applications to Text Indexing and String Matching], ''SIAM Journal on Computing,'' 35(2), 2005, 378–407.</ref>

| last1 = Blumer | first1 = Anselm

* [[FM-index]]

| last2 = Blumer | first2 = J.

* [[LZ-index]]

| last3 = Ehrenfeucht | first3 = Andrzej | author3-link = Andrzej Ehrenfeucht

| last4 = Haussler | first4 = David | author4-link = David Haussler

| last5 = McConnell | first5 = Ross M.

| editor-last = Paredaens | editor-first = Jan

| contribution = Building the minimal DFA for the set of all subwords of a word on-line in linear time

| doi = 10.1007/3-540-13345-3_9

| pages = 109–118

| publisher = Springer

| series = Lecture Notes in Computer Science

| title = Automata, Languages and Programming, 11th Colloquium, Antwerp, Belgium, July 16–20, 1984, Proceedings

| volume = 172

| year = 1984| isbn = 978-3-540-13345-2

}}</ref>

* The [[suffix array]], a sorted array of the starting positions of suffixes of the string, allowing substring search to be performed by [[binary search]]<ref name=bst/><ref name=gv/> Augmenting a suffix array with an [[LCP array]] of the lengths of common prefixes of consecutive suffixes allows the search to be performed symbol-by-symbol, matching the search time of the suffix tree.<ref>{{citation

| last1 = Manber | first1 = Udi | author1-link = Udi Manber

| last2 = Myers | first2 = Gene | author2-link = Eugene Myers

| doi = 10.1137/0222058

| issue = 5

| journal = [[SIAM Journal on Computing]]

| mr = 1237156

| pages = 935–948

| title = Suffix arrays: a new method for on-line string searches

| volume = 22

| year = 1993}}</ref>

* The [[compressed suffix array]], a data structure that combines [[data compression]] with the suffix array, allowing the structure to be stored in space sublinear in the text length<ref name=bst/><ref name=gv>{{citation

| last1 = Grossi | first1 = Roberto

| last2 = Vitter | first2 = Jeffrey Scott | author2-link = Jeffrey Vitter

| doi = 10.1137/S0097539702402354

| issue = 2

| journal = SIAM Journal on Computing

| mr = 2191449

| pages = 378–407

| title = Compressed suffix arrays and suffix trees with applications to text indexing and string matching

| url = https://www.di.unipi.it/~grossi/PAPERS/sicomp05.pdf

| volume = 35

| year = 2005| hdl = 1808/18962

}}</ref>

* The [[FM-index]], another compressed substring index based on the [[Burrows–Wheeler transform]] and closely related to the suffix array<ref>{{citation

| last1 = Ferragina | first1 = Paolo

| last2 = Manzini | first2 = Giovanni

| doi = 10.1145/1082036.1082039

| issue = 4

| journal = [[Journal of the ACM]]

| mr = 2164632

| pages = 552–581

| title = Indexing compressed text

| volume = 52

| year = 2005}}</ref>

== References ==

{{reflist}}

{{Strings|state=collapsed}}

[[Category:Algorithms on strings]]

[[Category:String data structures]]