Quantum Algorithm for the Shortest Superstring Problem
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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=(s^1,…,s^n) 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^*(1.728^n). Here O^* notation does not consider polynomials of n and the length of t.
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