I assume you're referring to the "missing satellites problem." This problem is already essentially solved:
1. Newer, more sensitive surveys have detected more Milky Way satellite galaxies.
2. Reionization and supernova feedback quench star formation in small dark matter halos, meaning that the smallest dark matter halos never form galaxies.
> See the review I linked.
I think we've talked about this elsewhere on HN before, and I pointed out that the paper you're linking to gets a lot of things wrong and is published in an obscure journal (presumably because it wouldn't survive peer review at any of the major journals).