Quantum Algorithms For String Problems
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Jin_cejin_SM_EECS_2022_thesis.pdf
Description
Thesis PDF
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Author(s)
Jin, Ce
Advisor(s)
Williams, Virginia Vassilevska
Williams, R. Ryan
Date Issued
September 2022
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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