Swiftly computing center strings
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
The bounded search tree algorithm for the closest string problem has quadratic smoothed complexity
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
A three-string approach to the closest string problem
Journal of Computer and System Sciences
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
On approximating string selection problems with outliers
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
The parameterized complexity of the shared center problem
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Enumerating neighbour and closest strings
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Configurations and minority in the string consensus problem
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
An efficient two-phase ant colony optimization algorithm for the closest string problem
SEAL'12 Proceedings of the 9th international conference on Simulated Evolution and Learning
On approximating string selection problems with outliers
Theoretical Computer Science
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The closest string problem and the closest substring problem are all natural theoretical computer science problems and find important applications in computational biology. Given $n$ input strings, the closest string (substring) problem finds a new string within distance $d$ to (a substring of) each input string and such that $d$ is minimized. Both problems are NP-complete. In this paper we propose new algorithms for these two problems. For the closest string problem, we developed an exact algorithm with time complexity $O(n|\Sigma|^{O(d)})$, where $\Sigma$ is the alphabet. This improves the previously best known result $O(nd^{O(d)})$ and results into a polynomial time algorithm when $d=O(\log n)$. By using this algorithm, a polynomial time approximation scheme (PTAS) for the closest string problem is also given with time complexity $O(n^{O(\epsilon^{-2})})$, improving the previously best known $O(n^{O(\epsilon^{-2}\log\frac{1}{\epsilon})})$ PTAS. A new algorithm for the closest substring problem is also proposed. Finally, we prove that a restricted version of the closest substring problem has the same parameterized complexity as the closest substring, answering an open question in the literature.