Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems

• Published in: arXiv.org
• Main Authors: Khadiev, Kamil, Bosch Machado, Carlos Manuel, Chen, Zeyu, Wu, Junde
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 31.12.2023
• Subjects: Algorithms; Assembling; Computer Science - Data Structures and Algorithms; Dictionaries; Physics - Quantum Physics; Strings
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2306.10572

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 \(O(n^3 1.728^n +L +\sqrt{L}n^{1.5}+\sqrt{L}n\log^2L\log^2n)\).