Quantum Algorithm for the Shortest Superstring Problem
This addresses a computational bottleneck in bioinformatics for reconstructing DNA sequences, but it is incremental as it builds on existing quantum approaches.
The paper tackles the Shortest Superstring Problem, which is relevant for DNA sequence assembly, by presenting a quantum algorithm with a running time of O*(1.728^n).
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 $S=(s^1,\dots,s^n)$ 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 $t$.