{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/147440"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/147440","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Quantum Algorithms For String Problems","abstract":"We design near-optimal quantum query algorithms for two important text processing problems: Longest Common Substring and Lexicographically Minimal String Rotation. Specifically, we show that: - Longest Common Substring can be solved by a quantum algorithm in Õ(n²⸍³) time, improving upon the Õ(n⁵⸍⁶)-time algorithm by Le Gall and Seddighin (2022). Moreover, given a length threshold 1 ≤ d ≤ n, our algorithm decides in n²⸍³⁺⁰⁽¹⁾/d¹⸍⁶ time whether the longest common substring has length at least d, almost matching the Omega(n²⸍³/d¹⸍⁶) quantum query lower bound. - Lexicographically Minimal String Rotation can be solved by a quantum algorithm in n¹⸍²⁺⁰⁽¹⁾ time, improving upon the Õ(n³⸍⁴)-time algorithm by Wang and Ying (2020), and almost matching the Ω(√n) quantum query lower bound. Our algorithm for Lexicographically Minimal String Rotation is obtained by speeding up a divide-and-conquer algorithm using nested Grover search and quantum minimum finding. Combining this divide-and-conquer idea with the deterministic sampling algorithm of Vishkin (1991) and Ramesh and Vinay (2003), we achieve a quantum speed-up of the String Synchronizing Set technique introduced by Kempa and Kociumaka (2019). Our algorithm for Longest Common Substring applies this string synchronizing set in the quantum walk framework.","abstract_html":"We design near-optimal quantum query algorithms for two important text processing problems: Longest Common Substring and Lexicographically Minimal String Rotation. Specifically, we show that: - Longest Common Substring can be solved by a quantum algorithm in Õ(n²⸍³) time, improving upon the Õ(n⁵⸍⁶)-time algorithm by Le Gall and Seddighin (2022). Moreover, given a length threshold 1 ≤ d ≤ n, our algorithm decides in n²⸍³⁺⁰⁽¹⁾/d¹⸍⁶ time whether the longest common substring has length at least d, almost matching the Omega(n²⸍³/d¹⸍⁶) quantum query lower bound. - Lexicographically Minimal String Rotation can be solved by a quantum algorithm in n¹⸍²⁺⁰⁽¹⁾ time, improving upon the Õ(n³⸍⁴)-time algorithm by Wang and Ying (2020), and almost matching the Ω(√n) quantum query lower bound. Our algorithm for Lexicographically Minimal String Rotation is obtained by speeding up a divide-and-conquer algorithm using nested Grover search and quantum minimum finding. Combining this divide-and-conquer idea with the deterministic sampling algorithm of Vishkin (1991) and Ramesh and Vinay (2003), we achieve a quantum speed-up of the String Synchronizing Set technique introduced by Kempa and Kociumaka (2019). Our algorithm for Longest Common Substring applies this string synchronizing set in the quantum walk framework.","abstract_has_math":false,"creators":["Jin, Ce"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science","school":null,"contributors":[],"advisors":["Williams, Virginia Vassilevska","Williams, R. Ryan"],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-09","date_published":"2022-09","updated_at":"2026-07-22T22:21:55Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"rights_urls":["http://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/147440","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Williams, Virginia Vassilevska","Williams, R. Ryan"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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Specifically, we show that: - Longest Common Substring can be solved by a quantum algorithm in Õ(n²⸍³) time, improving upon the Õ(n⁵⸍⁶)-time algorithm by Le Gall and Seddighin (2022). Moreover, given a length threshold 1 ≤ d ≤ n, our algorithm decides in n²⸍³⁺⁰⁽¹⁾/d¹⸍⁶ time whether the longest common substring has length at least d, almost matching the Omega(n²⸍³/d¹⸍⁶) quantum query lower bound. - Lexicographically Minimal String Rotation can be solved by a quantum algorithm in n¹⸍²⁺⁰⁽¹⁾ time, improving upon the Õ(n³⸍⁴)-time algorithm by Wang and Ying (2020), and almost matching the Ω(√n) quantum query lower bound. Our algorithm for Lexicographically Minimal String Rotation is obtained by speeding up a divide-and-conquer algorithm using nested Grover search and quantum minimum finding. Combining this divide-and-conquer idea with the deterministic sampling algorithm of Vishkin (1991) and Ramesh and Vinay (2003), we achieve a quantum speed-up of the String Synchronizing Set technique introduced by Kempa and Kociumaka (2019). Our algorithm for Longest Common Substring applies this string synchronizing set in the quantum walk framework."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Quantum Algorithms For String Problems"]}]}],"canonical_facts":{"dc:contributor.advisor":["Williams, Virginia Vassilevska","Williams, R. Ryan"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Jin, Ce"],"dc:date.accessioned":["2023-01-19T19:50:29Z"],"dc:date.available":["2023-01-19T19:50:29Z"],"dc:date.issued":["2022-09"],"dc:description.abstract":["We design near-optimal quantum query algorithms for two important text processing problems: Longest Common Substring and Lexicographically Minimal String Rotation. Specifically, we show that: - Longest Common Substring can be solved by a quantum algorithm in Õ(n²⸍³) time, improving upon the Õ(n⁵⸍⁶)-time algorithm by Le Gall and Seddighin (2022). Moreover, given a length threshold 1 ≤ d ≤ n, our algorithm decides in n²⸍³⁺⁰⁽¹⁾/d¹⸍⁶ time whether the longest common substring has length at least d, almost matching the Omega(n²⸍³/d¹⸍⁶) quantum query lower bound. - Lexicographically Minimal String Rotation can be solved by a quantum algorithm in n¹⸍²⁺⁰⁽¹⁾ time, improving upon the Õ(n³⸍⁴)-time algorithm by Wang and Ying (2020), and almost matching the Ω(√n) quantum query lower bound. Our algorithm for Lexicographically Minimal String Rotation is obtained by speeding up a divide-and-conquer algorithm using nested Grover search and quantum minimum finding. Combining this divide-and-conquer idea with the deterministic sampling algorithm of Vishkin (1991) and Ramesh and Vinay (2003), we achieve a quantum speed-up of the String Synchronizing Set technique introduced by Kempa and Kociumaka (2019). 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