A major advantage of the ILP is that it can be modified easily to incorporate additional chemical constraints or optimizations to obtain natural joins between two molecular fragments. This can be achieved by either adding penalties or by excluding structure such as allenes C C C by adding constraints on the neighborhoods in G and/or H for edges e ∈ B • . In such a weighted version, ILP solvers can efficiently produce limited top-lists of candidates without the need for an exhaustive enumeration and subsequent ranking.