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A theoretical and experimental analysis of BWT variants for string collections ...
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String Rearrangement Inequalities and a Total Order Between Primitive Words ...
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Dynamic Suffix Array with Polylogarithmic Queries and Updates ...
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An Optimal-Time RLBWT Construction in BWT-runs Bounded Space ...
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Suffix tree-based linear algorithms for multiple prefixes, single suffix counting and listing problems ...
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Reduction ratio of the IS-algorithm: worst and random cases ...
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HOLZ: High-Order Entropy Encoding of Lempel-Ziv Factor Distances ...
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A Note on the Performance of Algorithms for Solving Linear Diophantine Equations in the Naturals ...
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Lexicographically Fair Learning: Algorithms and Generalization ...
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Near-Optimal Quantum Algorithms for String Problems ...
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Abstract:
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology literature since the 1970s, and are known to be solvable by near-linear time classical algorithms. In this work, we give quantum algorithms for these problems with near-optimal query complexities and time complexities. Specifically, we show that: - Longest Common Substring can be solved by a quantum algorithm in $\tilde O(n^{2/3})$ time, improving upon the recent $\tilde O(n^{5/6})$-time algorithm by Le Gall and Seddighin (2020). Our algorithm uses the MNRS quantum walk framework, together with a careful combination of string synchronizing sets (Kempa and Kociumaka, 2019) and generalized difference covers. - Lexicographically Minimal String Rotation can be solved by a quantum algorithm in $n^{1/2 + o(1)}$ time, improving upon the recent $\tilde O(n^{3/4})$-time algorithm by ... : To appear in SODA 2022. Fixed cleveref issues ...
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Keyword:
Data Structures and Algorithms cs.DS; FOS Computer and information sciences; FOS Physical sciences; Quantum Physics quant-ph
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URL: https://arxiv.org/abs/2110.09696 https://dx.doi.org/10.48550/arxiv.2110.09696
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Dynamic Suffix Array with Sub-linear update time and Poly-logarithmic Lookup Time ...
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The Labeled Direct Product Optimally Solves String Problems on Graphs ...
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