Quantum Algorithm for Lexicographically Minimal String Rotation

• URL: http://arxiv.org/abs/2012.09376v3
• Date: Mon, 13 Nov 2023 13:38:00 GMT
• Title: Quantum Algorithm for Lexicographically Minimal String Rotation
• Authors: Qisheng Wang and Mingsheng Ying
• Abstract summary: Lexicographically minimal string rotation (LMSR) is a problem to find the minimal one among all rotations of a string in the lexicographical order. We propose an $O(n3/4)$ quantum query algorithm for LMSR.
• Score: 5.905222176603487
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Lexicographically minimal string rotation (LMSR) is a problem to find the minimal one among all rotations of a string in the lexicographical order, which is widely used in equality checking of graphs, polygons, automata and chemical structures. In this paper, we propose an $O(n^{3/4})$ quantum query algorithm for LMSR. In particular, the algorithm has average-case query complexity $O(\sqrt n \log n)$, which is shown to be asymptotically optimal up to a polylogarithmic factor, compared to its $\Omega\left(\sqrt{n/\log n}\right)$ lower bound. Furthermore, we show that our quantum algorithm outperforms any (classical) randomized algorithms in both worst and average cases. As an application, it is used in benzenoid identification and disjoint-cycle automata minimization.

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