4 We now give a Lagrangian relaxation algorithm for integration of a hypergraph with a bigram language model, in cases where the hypergraph satisfies the following simplifying assumption: Assumption 4.1 (The strict ordering assumption.)
for any two leaves v and w, it is either the case that: 1) for all derivations y such that v and w are both in the sequence l(y), v precedes w; or 2) for all derivations y such that v and w are both in l(y), w precedes v. under this assumption, the relative ordering of any two leaves is fixed.