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Quantum algorithm for the shortest superstring problem
K. Khadiev, C. Machado·December 26, 2021·DOI: 10.1117/12.2624618
EngineeringPhysicsComputer Science
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Abstract
In this paper, we consider the “Shortest Superstring Problem”(SSP) or the “Shortest Common Superstring Problem”(SCS). The problem is as follows. For a positive integer n, a sequence of n strings S = (s1, . . . , sn) is given. We should construct the shortest string t (we call it superstring) that contains each string from the given sequence as a substring. The problem is connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. We present a quantum algorithm with running time O∗(1.728n). Here O∗ notation does not consider polynomials of n and the length of t.