# Bracketing Encodings for 2-Planar Dependency Parsing

arXiv: https://arxiv.org/abs/2011.00596 · HTML: https://mlsanity.com/paper/2011.00596/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2020.

## Built on by (most cited first, 15 of 15)

- [A Modest Pareto Optimisation Analysis of Dependency Parsers in 2021](https://mlsanity.com/paper/2106.04216/) (2021)
- [4 and 7-bit Labeling for Projective and Non-Projective Dependency Trees](https://mlsanity.com/paper/2310.14319/) (2023)
- [Not All Linearizations Are Equally Data-Hungry in Sequence Labeling Parsing](https://mlsanity.com/paper/2108.07556/) (2021)
- [Linear-Time Modeling of Linguistic Structure: An Order-Theoretic Perspective](https://mlsanity.com/paper/2305.15057/) (2023)
- [Assessment of Pre-Trained Models Across Languages and Grammars](https://mlsanity.com/paper/2309.11165/) (2023)
- [On the Challenges of Fully Incremental Neural Dependency Parsing](https://mlsanity.com/paper/2309.16254/) (2023)
- [Dependency Graph Parsing as Sequence Labeling](https://mlsanity.com/paper/2410.17972/) (2024)
- [Splitting EUD graphs into trees: A quick and clatty approach](https://mlsanity.com/paper/2106.13155/) (2021)
- [Parsing linearizations appreciate PoS tags - but some are fussy about errors](https://mlsanity.com/paper/2210.15219/) (2022)
- [Hierarchical Bracketing Encodings for Dependency Parsing as Tagging](https://mlsanity.com/paper/2505.11693/) (2025)
- [Cross-lingual Inflection as a Data Augmentation Method for Parsing](https://mlsanity.com/paper/2205.09350/) (2022)
- [The Fragility of Multi-Treebank Parsing Evaluation](https://mlsanity.com/paper/2209.06699/) (2022)
- [Another Dead End for Morphological Tags? Perturbed Inputs and Parsing](https://mlsanity.com/paper/2305.15119/) (2023)
- [Growing Trees on Sounds: Assessing Strategies for End-to-End Dependency Parsing of Speech](https://mlsanity.com/paper/2406.12621/) (2024)
- [Formal Constraints on Dependency Syntax](https://mlsanity.com/paper/2604.04542/) (2026)

## Abstract (arXiv)

We present a bracketing-based encoding that can be used to represent any 2-planar dependency tree over a sentence of length n as a sequence of n labels, hence providing almost total coverage of crossing arcs in sequence labeling parsing. First, we show that existing bracketing encodings for parsing as labeling can only handle a very mild extension of projective trees. Second, we overcome this limitation by taking into account the well-known property of 2-planarity, which is present in the vast majority of dependency syntactic structures in treebanks, i.e., the arcs of a dependency tree can be split into two planes such that arcs in a given plane do not cross. We take advantage of this property to design a method that balances the brackets and that encodes the arcs belonging to each of those planes, allowing for almost unrestricted non-projectivity (round 99.9% coverage) in sequence labeling parsing. The experiments show that our linearizations improve over the accuracy of the original bracketing encoding in highly non-projective treebanks (on average by 0.4 LAS), while achieving a similar speed. Also, they are especially suitable when PoS tags are not used as input parameters to the models.