We study the generalization of maximum spanning tree dependency parsing to maximum acyclic subgraphs. Because the underlying optimization problem is intractable even under an arc-factored model, we consider the restriction to noncrossing dependency graphs. Our main contribution is a cubic-time exact inference algorithm for this class. We extend this algorithm into a practical parser and evaluate its performance on four linguistic data sets used in semantic dependency parsing. We also explore a generalization of our parsing framework to dependency graphs with pagenumber at most k and show that the resulting optimization problem is NP-hard for k ≥ 2.

We present a polynomial-time parsing algorithm for CCG, based on a new decomposition of derivations into small, shareable parts. Our algorithm has the same asymptotic complexity, O ( n 6 ), as a previous algorithm by Vijay-Shanker and Weir (1993), but is easier to understand, implement, and prove correct.

Head splitting techniques have been successfully exploited to improve the asymptotic runtime of parsing algorithms for projective dependency trees, under the arc-factored model. In this article we extend these techniques to a class of non-projective dependency trees, called well-nested dependency trees with block-degree at most 2, which has been previously investigated in the literature. We define a structural property that allows head splitting for these trees, and present two algorithms that improve over the runtime of existing algorithms at no significant loss in coverage.