Quantum jumbled pattern matching
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Let S_1, S_2 ∈Σ^* strings, we say that S_1 jumble match S_2 if they are permutations of each other. Given a text T of size N and a string S ∈Σ^*, the problem of Jumbled Pattern Matching (JPM) is to determine all substrings in T jumbled matching S. In classical computing, a widespread conjecture is that JPM requires Ω(N^2-ϵ) preprocessing time and space for O(1) query time, or Ω(N^1-δ) query time in the online version, with ϵ, δ >0. In this paper, we present a quantum algorithm for the online JPM in O(√(N)) time.
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