Network Querying and Copy Number Triplet Problems - ILP to the Rescue

We describe two biologically motivated problems where ILP seems to save the day.  The first is searching for the presences of a protein complex that is known in one species in another species network, using homology but no topology. Here an interesting application of connectivity in ILP comes up.  The second arises in cancer genomics: given two copy number profiles of a chromosome, find their common ancestor such that the total number of segmental duplications and deletions between the ancestor and the two profiles is minimum. Here ILP formulation is rather straightforward, but a more compact instance can be formulated.