Reoptimization of the Closest Substring Problem under Pattern Length Modification

Œis 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 llength closest substring of a given set of sequences S. How can this information be bene€cial 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. CCS CONCEPTS •Mathematics of computing→Combinatorial optimization; Approximation algorithms;