You have an extensive library of genomic DNA fragments, prepared by the use of restriction nucleases. You know their sequences and sizes and you have an assay to reliably separate and identify them by electrophoresis on agarose gels. It has been reported that a newly isolated protein forms tight complexes with some of the DNA fragments.
If you can identify those DNA fragments, you might be able make a very educated "guess" as to the identity of the gene that is regulated by the protein. You do not yet have the sequence and structural information about the protein, so bioinformatics approaches are not going to be especially useful. How would you proceed? Be clear as to what type of assay(s)) you would do, and specifically how you could use the protein, and an antibody to the protein to identify candidate DNA fragments/genes.