  This study investigates whether reoptimization can help in solving the
closest substring problem. We are dealing with the following reoptimization
scenario. Suppose, we have an optimal l-length closest substring of a given set
of sequences S. How can this information be beneficial in obtaining an
(l+k)-length closest substring for S? In this study, we show that the problem
is still computationally hard even with k=1. We present greedy approximation
algorithms that make use of the given information and prove that it has an
additive error that grows as the parameter k increases. Furthermore, we present
hard instances for each algorithm to show that the computed approximation ratio
is tight. We also show that we can slightly improve the running-time of the
existing polynomial-time approximation scheme (PTAS) for the original problem
through reoptimization.
