Inter-dependencies among ordering decisions within different constituents (e.g., for achieving parallelism) make the global sentence ordering problem challenging and are certainly worth investigating in future work.
for the present, we constrain the possible model types considered here by assuming that the ordering of any constituent is independent of the ordering within other constituents in the tree, including its daughters; consequently, ( ) ( ) Given this independence assumption, the only possible ordered trees are trees built with nonterminal constituents computed as follows: for each ( ) In fact, we can further constrain our search for the best ordering of each unordered constituent B, since C's head must match B's head: we have reduced the problem to finding the best ordering of each constituent of the unordered tree.