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arXiv · 2306.10572

Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems

Kamil Khadiev·Carlos Manuel Bosch Machado·Zeyu Chen·Junde Wu
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Abstract

In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the problem is assembling $t$ from the dictionary. The second version is the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). In this case, $t$ is not given, and we should construct the shortest string (we call it superstring) that contains each string from the given sequence as a substring. These problems are connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. For both problems, we suggest new quantum algorithms that work better than their classical counterparts. In the first case, we present a quantum algorithm with $O(m+\log m\sqrt{nL})$ running time. In the case of SSP, we present a quantum algorithm with running time $O(n^3 1.728^n +L +\sqrt{L}n^{1.5}+\sqrt{L}n\log^2L\log^2n)$.

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Kamil Khadiev, Carlos Manuel Bosch Machado, Zeyu Chen, Junde Wu. 2023-06-18. Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems. https://doi.org/10.26421/qic24.3-4-4

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