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arXiv · 2203.00164

Quantum jumbled pattern matching

Julio Juárez-Xochitemol·Edgar Chávez
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Abstract

Let $S_1, S_2 \in \Sigma^*$ strings, we say that $S_1$ {\em jumble match} $S_2$ if they are permutations of each other. Given a text $T$ of size $N$ and a string $S \in \Sigma^*$, the problem of \emph{Jumbled Pattern Matching} (JPM) is to determine all substrings in $T$ jumbled matching $S$. In classical computing, a widespread conjecture is that JPM requires $\Omega(N^{2-\epsilon})$ preprocessing time and space for $O(1)$ query time, or $\Omega(N^{1-\delta})$ query time in the online version, with $\epsilon, \delta >0$. In this paper, we present a quantum algorithm for the online JPM in $O(\sqrt{N})$ time.

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Julio Juárez-Xochitemol, Edgar Chávez. 2022-03-01. Quantum jumbled pattern matching. https://arxiv.org/abs/2203.00164

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