
Fast Classical and Quantum Algorithms for Online kserver Problem on Trees
We consider online algorithms for the kserver problem on trees. Chrobak...
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Quantum Query Complexity of Dyck Languages with Bounded Height
We consider the problem of determining if a sequence of parentheses is w...
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Space efficient quantum algorithms for mode, minentropy and kdistinctness
We study the problem of determining if the mode of the output distributi...
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InstanceOptimality in the Noisy Valueand ComparisonModel  Accept, Accept, Strong Accept: Which Papers get in?
Motivated by crowdsourced computation, peergrading, and recommendation ...
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Quantum QuerytoCommunication Simulation Needs a Logarithmic Overhead
Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean f...
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Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error
We investigate the randomized and quantum communication complexities of ...
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A nearoptimal directsum theorem for communication complexity
We show a near optimal directsum theorem for the twoparty randomized c...
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Quantum Algorithm for Lexicographically Minimal String Rotation
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 averagecase query complexity O(√(n)log n), which is shown to be asymptotically optimal up to a polylogarithmic factor, compared with its Ω(√(n/log n)) lower bound. Furthermore, we claim that our quantum algorithm outperforms any (classical) randomized algorithms in both worstcase and averagecase query complexities by showing that every (classical) randomized algorithm for LMSR has worstcase query complexity Ω(n) and averagecase query complexity Ω(n/log n). Our quantum algorithm for LMSR is developed in a framework of nested quantum algorithms, based on two new results: (i) an O(√(n)) (optimal) quantum minimum finding on boundederror quantum oracles; and (ii) its O(√(n log(1/ε))) (optimal) error reduction. As a byproduct, we obtain some better upper bounds of independent interest: (i) O(√(N)) (optimal) for constantdepth MINMAX trees on N variables; and (ii) O(√(n log m)) for pattern matching which removes polylog(n) factors.
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