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We introduce a novel chart-based algorithm for span-based parsing ofdiscontinuous constituency trees of block degree two, including ill-nestedstructures. In particular, we show that we can build variants of our parserwith smaller search spaces and time complexities ranging from $\mathcal O(n^6)$down to $\mathcal O(n^3)$. The cubic time variant covers 98\% of constituentsobserved in linguistic treebanks while having the same complexity as continuousconstituency parsers. We evaluate our approach on German and English treebanks(Negra, Tiger and Discontinuous PTB) and report state-of-the-art results in thefully supervised setting. We also experiment with pre-trained word embeddingsand \bert{}-based neural networks.

Span-based discontinuous constituency parsing: a family of exact chart-based algorithms with time complexities from O(n^6) down to O(n^3)