We present a novel dependency parsing method which enforces two structural properties on dependency trees: bounded block degree and well-nestedness. These properties are useful to better represent the set of admissible dependency structures in treebanks and connect dependency parsing to context-sensitive grammatical formalisms. We cast this problem as an Integer Linear Program that we solve with Lagrangian Relaxation from which we derive a heuristic and an exact method based on a Branch-and-Bound search. Experimentally, we see that these methods are efficient and competitive compared to a baseline unconstrained parser, while enforcing structural properties in all cases.
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