Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911826832261120 |
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| author | Khadiev, Kamil Machado, Carlos Manuel Bosch Chen, Zeyu Wu, Junde |
| author_facet | Khadiev, Kamil Machado, Carlos Manuel Bosch Chen, Zeyu Wu, Junde |
| contents | 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 $O(n^3 1.728^n +L +\sqrt{L}n^{1.5}+\sqrt{L}n\log^2L\log^2n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10572 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems Khadiev, Kamil Machado, Carlos Manuel Bosch Chen, Zeyu Wu, Junde Quantum Physics Data Structures and Algorithms 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 $O(n^3 1.728^n +L +\sqrt{L}n^{1.5}+\sqrt{L}n\log^2L\log^2n)$. |
| title | Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2306.10572 |