A 2-approximation algorithm for the contig-based genomic scaffold filling problem.

The genomic scaffold filling problem has attracted a lot of attention recently. The problem is on filling an incomplete sequence (scaffold) I into I', with respect to a complete reference genome G, such that the number of common/shared adjacencies between G and I' is maximized. The problem is NP-complete, and admits a constant-factor approximation. However, the sequence input I is not quite practical and does not fit most of the real datasets (where a scaffold is more often given as a list of contigs). In this paper, we revisit the genomic scaffold filling problem by considering this important case when a scaffold S is given, the missing genes can only be inserted in between the contigs, and the objective is to maximize the number of common adjacencies between G and the filled genome S'. For this problem, we present a simple NP-completeness proof, we then present a factor-2 approximation algorithm.