Motivated by the trend of genome sequencing without completing the sequence of the whole genomes, Mu˜noz et al. recently studied the problem of filling an incomplete multichromosomal genome (or scaffold) I with respect to a complete target genome G such that the resulting genomic distance between I′ and G is minimized, where I′ is the corresponding filled scaffold. We call this problem the one-sided scaffold filling problem. In this paper, we follow Mu˜noz et al. to investigate the scaffold filling problem under the breakpoint distance for the simplest unichromosomal genomes. When the input genome contains no gene repetition (i.e., is a fragment of a permutation), we show that the two-sided scaffold filling problem is polynomially solvable. However, when the input genome contains some genes which appear twice, even the one-sided scaffold filling problem becomes NP-complete. Finally, using the ideas for solving the two-sided scaffold filling problem under the breakpoint dis...