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.

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