[math-fun] Packing complexity question

Responses to my MO post http://mathoverflow.net/questions/232165/one-dimensional-packing-of-monomers... haven't taught me anything. Do any of you know (or can any of you figure out) how difficult packing problems of this kind are, from a complexity standpoint? If S is held fixed, then F(n,S) is polynomial time, but that's not very interesting; I want to know what happens as S varies. Jim Propp