Carlos Gomez-Rodriguez, David Weir and John Carroll
We present novel parsing algorithms for several sets of mildly non-projective dependency structures. First, we define a parser for well-nested structures of gap degree at most 1, with the same complexity as the best existing parsers for constituency formalisms of equivalent generative power. We then extend this algorithm to handle all well-nested structures with gap degree bounded by any constant k. Finally, we define a parsing algorithm for a new class of structures with gap degree up to k that includes some ill-nested structures. This set of structures, which we call mildly ill-nested, includes all the gap degree k structures in a number of dependency treebanks.