Abstract
In this paper, we compute the first linear kernel for the complementary problem of Maximal Strip Recovery (CMSR) — an NP-hard 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 (for the method) 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 78k kernel for the problem, which is again tight for the method. Combined with the known algorithm using bounded degree search, we obtain the best Fixed-Parameterized-Tractable algorithm for CMSR to this date, running in O(2.36kk2+n2) time.
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