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We introduce a novel chart-based algorithm for span-based parsing of discontinuous constituency trees of block degree two, including ill-nested structures. In particular, we show that we can build variants of our parser with 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 constituents observed in linguistic treebanks while having the same complexity as continuous constituency parsers. We evaluate our approach on German and English treebanks (Negra, Tiger and Discontinuous PTB) and report state-of-the-art results in the fully supervised setting. We also experiment with pre-trained word embeddings and \bert{}-based neural networks.

Span-based discontinuous constituency parsing: a family of exact chart-based algorithms with time complexities from O(nˆ6) down to O(nˆ3)