Background: The center string (or closest string) problem is a classic computer science problem with important applications in computational biology. Given k input strings and a distance threshold d, we search for a string within Hamming distance at most d to each input string. This problem is NP complete.
Results: In this paper, we focus on exact methods for the problem that are also swift in application. We first introduce data reduction techniques that allow us to infer that certain instances have no solution, or that a center string must satisfy certain conditions. We describe how to use this information to speed up two previously published search tree algorithms. Then, we describe a novel iterative search strategy that is efficient in practice, where some of our reduction techniques can also be applied. Finally, we present results of an evaluation study for two different data sets from a biological application.
Conclusions: We find that the running time for computing the optimal center string is dominated by the subroutine calls for d = dopt -1 and d = dopt. Our data reduction is very effective for both, either rejecting unsolvable instances or solving trivial positions. We find that this speeds up computations considerably.