The Query Complexity of Finding a Hidden Permutation

Abstract

We study the query complexity of determining a hidden permutation. More specifically, we study the problem of learning a secret (z,π) consisting of a binary string z of length n and a permutation π of [n]. The secret must be unveiled by asking queries x ∈ {0,1}n, and for each query asked, we are returned the score fz,π(x) defined as fz,π(x) := max{i ∈ [0..n] | ∀ j ≤ i : zπ( j) = xπ( j)} ; i.e., the length of the longest common prefix of x and z with respect to π . The goal is to minimize the number of queries asked. We prove matching upper and lower bounds for the deterministic and randomized query complexity of Θ(n logn) and Θ(n log logn), respectively. Mathematics Subject Classification: 68R05 (Computer Science.Combinatorics), 68W20 (Computer Science.Randomized Algorithms), 68W40 (Computer Science.Analysis of Algorithms)

DOI: 10.1007/978-3-642-40273-9_1

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Cite this paper

@inproceedings{Afshani2013TheQC, title={The Query Complexity of Finding a Hidden Permutation}, author={Peyman Afshani and Manindra Agrawal and Benjamin Doerr and Carola Doerr and Kasper Green Larsen and Kurt Mehlhorn}, booktitle={Space-Efficient Data Structures, Streams, and Algorithms}, year={2013} }