Abstract
AbstractLexicographically 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 $$O(n^{3/4})$$
O
(
n
3
/
4
)
quantum query algorithm for LMSR. In particular, the algorithm has average-case query complexity $$O(\sqrt{n} \log n)$$
O
(
n
log
n
)
, which is shown to be asymptotically optimal up to a polylogarithmic factor, compared to its $$\Omega \left( \sqrt{n/\log n}\right) $$
Ω
n
/
log
n
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.
Funder
MEXT Quantum Leap Flagship Program
National Key Research and Development Program of China
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Theoretical Computer Science
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