A linear kernel for the complementary maximal strip recovery problem

Abstract

In this paper, we compute the first linear kernel for the complementary problem of Maximal Strip Recovery (CMSR) - a well-known NP-complete problem in computational genomics. Let k be the parameter which represents the size of the solution. The core of the technique is to first obtain a tight 18k bound on the parameterized solution search space, which is done through a mixed global rules and local rules, and via an inverse amortized analysis. Then we apply additional data-reduction rules to obtain a tight 84k kernel for the problem. Combined with the known algorithm using bounded degree search, we obtain the best FPT algorithm for CMSR to this date, running in O(2.36 k k 2 + n 2) time. © 2012 Springer-Verlag.