A Three-Stage Algorithm for the Closest String Problem on Artificial and Real Gene Sequences

The Closest String Problem is an NP-hard problem that aims to find a string that has the minimum distance from all sequences that belong to the given set of strings. Its applications can be found in coding theory, computational biology, and designing degenerated primers, among others. There are efficient exact algorithms that have reached high-quality solutions for binary sequences. However, there is still room for improvement concerning the quality of solutions over DNA and protein sequences. In this paper, we introduce a three-stage algorithm that comprises the following process: first, we apply a novel alphabet pruning method to reduce the search space for effectively finding promising search regions. Second, a variant of beam search to find a heuristic solution is employed. This method utilizes a newly developed guiding function based on an expected distance heuristic score of partial solutions. Last, we introduce a local search to improve the quality of the solution obtained from the beam search. Furthermore, due to the lack of real-world benchmarks, two real-world datasets are introduced to verify the robustness of the method. The extensive experimental results show that the proposed method outperforms the previous approaches from the literature.