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<title>Substring index</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Substring index</span></span>

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<p>In <a href="Computer_science" title="Computer science">computer science</a>, a <b>substring index</b> is a <a href="Data_structure" title="Data structure">data structure</a> which gives <a href="Substring" title="Substring">substring</a> search in a text or text collection in <a href="Sublinear" class="mw-redirect" title="Sublinear">sublinear</a> time. Once constructed from a document or set of documents, a substring index can be used to locate all occurrences of a pattern in time linear or near-linear in the pattern size, with no dependence or only logarithmic dependence on the document size.<sup id="cite_ref-bst_1-0" class="reference"><a href="#cite_note-bst-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>The phrase <b>full-text index</b> is often used for substring indexes. But this is ambiguous, as it is also used for regular word indexes such as <a href="Inverted_file" class="mw-redirect" title="Inverted file">inverted files</a> and <a href="Document_retrieval" title="Document retrieval">document retrieval</a>. See <a href="Full_text_search" class="mw-redirect" title="Full text search">full text search</a>.

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<div class="mw-heading mw-heading2"><h2 id="General_considerations">General considerations</h2></div>

<p>These data structures typically treat their text and pattern as <a href="String_(computer_science)" title="String (computer science)">strings</a> 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 <a href="Unicode" title="Unicode">Unicode</a>) but in practical applications for <a href="Text_retrieval" class="mw-redirect" title="Text retrieval">text retrieval</a> it may be preferable to treat the (<a href="Stemming" title="Stemming">stemmed</a>) 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.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2></div>

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

</p>

<ul><li>The <a href="Suffix_tree" title="Suffix tree">suffix tree</a>, a <a href="Radix_tree" title="Radix tree">radix tree</a> of the suffixes of the string, allowing substring search to be performed symbol-by-symbol<sup id="cite_ref-bst_1-1" class="reference"><a href="#cite_note-bst-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gv_3-0" class="reference"><a href="#cite_note-gv-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li>

<li>The <a href="Suffix_automaton" title="Suffix automaton">suffix automaton</a>, the minimal <a href="Deterministic_finite_automaton" title="Deterministic finite automaton">deterministic finite automaton</a> that recognizes substrings of a given text, closely related to the suffix tree and constructable by variants of the same algorithms.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li>

<li>The <a href="Suffix_array" title="Suffix array">suffix array</a>, a sorted array of the starting positions of suffixes of the string, allowing substring search to be performed by <a href="Binary_search" title="Binary search">binary search</a><sup id="cite_ref-bst_1-2" class="reference"><a href="#cite_note-bst-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gv_3-1" class="reference"><a href="#cite_note-gv-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Augmenting a suffix array with an <a href="LCP_array" title="LCP array">LCP array</a> 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.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li>

<li>The <a href="Compressed_suffix_array" title="Compressed suffix array">compressed suffix array</a>, a data structure that combines <a href="Data_compression" title="Data compression">data compression</a> with the suffix array, allowing the structure to be stored in space sublinear in the text length<sup id="cite_ref-bst_1-3" class="reference"><a href="#cite_note-bst-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gv_3-2" class="reference"><a href="#cite_note-gv-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li>

<li>The <a href="FM-index" title="FM-index">FM-index</a>, another compressed substring index based on the <a href="Burrows%E2%80%93Wheeler_transform" title="Burrows–Wheeler transform">Burrows–Wheeler transform</a> and closely related to the suffix array<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFBarskyStegeThomo2012" class="citation cs2">Barsky, Marina; Stege, Ulrike; Thomo, Alex (2012), "Chapter 1: Structures for Indexing Substrings", <i>Full-Text (Substring) Indexes in External Memory</i>, Synthesis Lectures on Data Management, Springer International Publishing, pp. <span class="nowrap">1–</span>15, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-031-01885-5_1">10.1007/978-3-031-01885-5_1</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9783031018855</bdi></cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFRisvik1998" class="citation cs2">Risvik, Knut Magne (1998), "Approximate word sequence matching over sparse suffix trees", in <a href="Martin_Farach-Colton" title="Martin Farach-Colton">Farach-Colton, Martin</a> (ed.), <i>Combinatorial Pattern Matching, 9th Annual Symposium, CPM 98, Piscataway, New Jersey, USA, July 20–22, 1998, Proceedings</i>, Lecture Notes in Computer Science, vol. 1448, Springer, pp. <span class="nowrap">65–</span>79, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBFB0030781">10.1007/BFB0030781</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-64739-3</bdi></cite></span>

</li>

<li id="cite_note-gv-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-gv_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-gv_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-gv_3-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFGrossiVitter2005" class="citation cs2">Grossi, Roberto; <a href="Jeffrey_Vitter" title="Jeffrey Vitter">Vitter, Jeffrey Scott</a> (2005), <a rel="nofollow" class="external text" href="https://www.di.unipi.it/~grossi/PAPERS/sicomp05.pdf">"Compressed suffix arrays and suffix trees with applications to text indexing and string matching"</a> <span class="cs1-format">(PDF)</span>, <i>SIAM Journal on Computing</i>, <b>35</b> (2): <span class="nowrap">378–</span>407, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2FS0097539702402354">10.1137/S0097539702402354</a>, <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1808%2F18962">1808/18962</a>, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=2191449">2191449</a></cite></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFBlumerBlumerEhrenfeuchtHaussler1984" class="citation cs2">Blumer, Anselm; Blumer, J.; <a href="Andrzej_Ehrenfeucht" title="Andrzej Ehrenfeucht">Ehrenfeucht, Andrzej</a>; <a href="David_Haussler" title="David Haussler">Haussler, David</a>; McConnell, Ross M. (1984), "Building the minimal DFA for the set of all subwords of a word on-line in linear time", in Paredaens, Jan (ed.), <i>Automata, Languages and Programming, 11th Colloquium, Antwerp, Belgium, July 16–20, 1984, Proceedings</i>, Lecture Notes in Computer Science, vol. 172, Springer, pp. <span class="nowrap">109–</span>118, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-13345-3_9">10.1007/3-540-13345-3_9</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-13345-2</bdi></cite></span>

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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFManberMyers1993" class="citation cs2"><a href="Udi_Manber" title="Udi Manber">Manber, Udi</a>; <a href="Eugene_Myers" title="Eugene Myers">Myers, Gene</a> (1993), "Suffix arrays: a new method for on-line string searches", <i><a href="SIAM_Journal_on_Computing" title="SIAM Journal on Computing">SIAM Journal on Computing</a></i>, <b>22</b> (5): <span class="nowrap">935–</span>948, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F0222058">10.1137/0222058</a>, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1237156">1237156</a></cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFFerraginaManzini2005" class="citation cs2">Ferragina, Paolo; Manzini, Giovanni (2005), "Indexing compressed text", <i><a href="Journal_of_the_ACM" title="Journal of the ACM">Journal of the ACM</a></i>, <b>52</b> (4): <span class="nowrap">552–</span>581, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F1082036.1082039">10.1145/1082036.1082039</a>, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=2164632">2164632</a></cite></span>

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</style><div id="Strings176" style="font-size:114%;margin:0 4em"><a href="String_(computer_science)" title="String (computer science)">Strings</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="String_metric" title="String metric">String metric</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Approximate_string_matching" title="Approximate string matching">Approximate string matching</a></li>

<li><a href="Bitap_algorithm" title="Bitap algorithm">Bitap algorithm</a></li>

<li><a href="Damerau%E2%80%93Levenshtein_distance" title="Damerau–Levenshtein distance">Damerau–Levenshtein distance</a></li>

<li><a href="Edit_distance" title="Edit distance">Edit distance</a></li>

<li><a href="Gestalt_pattern_matching" title="Gestalt pattern matching">Gestalt pattern matching</a></li>

<li><a href="Hamming_distance" title="Hamming distance">Hamming distance</a></li>

<li><a href="Jaro%E2%80%93Winkler_distance" title="Jaro–Winkler distance">Jaro–Winkler distance</a></li>

<li><a href="Lee_distance" title="Lee distance">Lee distance</a></li>

<li><a href="Levenshtein_automaton" title="Levenshtein automaton">Levenshtein automaton</a></li>

<li><a href="Levenshtein_distance" title="Levenshtein distance">Levenshtein distance</a></li>

<li><a href="Wagner%E2%80%93Fischer_algorithm" title="Wagner–Fischer algorithm">Wagner–Fischer algorithm </a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="String-searching_algorithm" title="String-searching algorithm">String-searching algorithm</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Apostolico%E2%80%93Giancarlo_algorithm" title="Apostolico–Giancarlo algorithm">Apostolico–Giancarlo algorithm</a></li>

<li><a href="Boyer%E2%80%93Moore_string-search_algorithm" title="Boyer–Moore string-search algorithm">Boyer–Moore string-search algorithm</a></li>

<li><a href="Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm" title="Boyer–Moore–Horspool algorithm">Boyer–Moore–Horspool algorithm</a></li>

<li><a href="Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm" title="Knuth–Morris–Pratt algorithm">Knuth–Morris–Pratt algorithm</a></li>

<li><a href="Rabin%E2%80%93Karp_algorithm" title="Rabin–Karp algorithm">Rabin–Karp algorithm</a></li>

<li><a href="Raita_algorithm" title="Raita algorithm">Raita algorithm</a></li>

<li><a href="Trigram_search" title="Trigram search">Trigram search</a></li>

<li><a href="Two-way_string-matching_algorithm" title="Two-way string-matching algorithm">Two-way string-matching algorithm</a></li>

<li><a href="Zhu%E2%80%93Takaoka_string_matching_algorithm" title="Zhu–Takaoka string matching algorithm">Zhu–Takaoka string matching algorithm</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Multiple string searching</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aho%E2%80%93Corasick_algorithm" title="Aho–Corasick algorithm">Aho–Corasick</a></li>

<li><a href="Commentz-Walter_algorithm" title="Commentz-Walter algorithm">Commentz-Walter algorithm</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Regular_expression" title="Regular expression">Regular expression</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Comparison_of_regular-expression_engines" class="mw-redirect" title="Comparison of regular-expression engines">Comparison of regular-expression engines</a></li>

<li><a href="Regular_grammar" title="Regular grammar">Regular grammar</a></li>

<li><a href="Thompson's_construction" title="Thompson's construction">Thompson's construction</a></li>

<li><a href="Nondeterministic_finite_automaton" title="Nondeterministic finite automaton">Nondeterministic finite automaton</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Sequence_alignment" title="Sequence alignment">Sequence alignment</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="BLAST_(biotechnology)" title="BLAST (biotechnology)">BLAST</a></li>

<li><a href="Hirschberg's_algorithm" title="Hirschberg's algorithm">Hirschberg's algorithm</a></li>

<li><a href="Needleman%E2%80%93Wunsch_algorithm" title="Needleman–Wunsch algorithm">Needleman–Wunsch algorithm</a></li>

<li><a href="Smith%E2%80%93Waterman_algorithm" title="Smith–Waterman algorithm">Smith–Waterman algorithm</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Data_structure" title="Data structure">Data structure</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Deterministic_acyclic_finite_state_automaton" title="Deterministic acyclic finite state automaton">DAFSA</a></li>

<li>

<ul><li><a href="Suffix_array" title="Suffix array">Suffix array</a></li>

<li><a href="Suffix_automaton" title="Suffix automaton">Suffix automaton</a></li>

<li><a href="Suffix_tree" title="Suffix tree">Suffix tree</a></li>

<li><a href="Compressed_suffix_array" title="Compressed suffix array">Compressed suffix array</a></li>

<li><a href="LCP_array" title="LCP array">LCP array</a></li>

<li><a href="FM-index" title="FM-index">FM-index</a></li></ul></li>

<li><a href="Generalized_suffix_tree" title="Generalized suffix tree">Generalized suffix tree</a></li>

<li><a href="Ternary_search_tree" title="Ternary search tree">Ternary search tree</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Parsing" title="Parsing">Parsing</a></li>

<li><a href="Pattern_matching" title="Pattern matching">Pattern matching</a></li>

<li><a href="Compressed_pattern_matching" title="Compressed pattern matching">Compressed pattern matching</a></li>

<li><a href="Longest_common_subsequence" title="Longest common subsequence">Longest common subsequence</a></li>

<li><a href="Longest_common_substring" title="Longest common substring">Longest common substring</a></li>

<li><a href="Sequential_pattern_mining" title="Sequential pattern mining">Sequential pattern mining</a></li>

<li>Sorting</li>

<li><a href="Semi-Thue_system" title="Semi-Thue system">String rewriting systems</a></li>

<li><a href="String_operations" title="String operations">String operations</a></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-01-10" href="https://en.wikipedia.org/wiki/?title=Substring_index&oldid=1268543610">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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