2013
DOI: 10.1162/tacl_a_00206
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Finding Optimal 1-Endpoint-Crossing Trees

Abstract: Dependency parsing algorithms capable of producing the types of crossing dependencies seen in natural language sentences have traditionally been orders of magnitude slower than algorithms for projective trees. For 95.8–99.8% of dependency parses in various natural language treebanks, whenever an edge is crossed, the edges that cross it all have a common vertex. The optimal dependency tree that satisfies this 1-Endpoint-Crossing property can be found with an O( n4) parsing algorithm that recursively combines fo… Show more

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Cited by 39 publications
(68 citation statements)
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References 13 publications
(17 reference statements)
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“…Such dependencies are interesting because while they exist across languages, they are nevertheless rare (Ferrer‐i Cancho, 2006; Straka, Hajic, Straková, & Hajic, 2015), and they help in understanding formal properties of natural languages (Joshi, 1985; Kuhlmann & Möhl, 2007; Shieber, 1985). More importantly, they are difficult for computational parsers (Gómez‐Rodríguez, Weir, & Carroll, 2009; Kübler et al, 2009; Kuhlmann & Satta, 2009; McDonald & Satta, 2007; Nederhof, 1999; Neuhaus & Bröker, 1997; Nivre, 2009; Pitler, Kannan, & Marcus, 2013; Vijay‐Shankar & Joshi, 1985), and they are known to pose difficulty for humans (Boland, Tanenhaus, Garnsey, & Carlson, 1995; Husain & Vasishth, 2015; Levy et al, 2012; Traxler & Pickering, 1996; Yadav, Vaidya, & Husain, 2017).…”
Section: Methodsmentioning
confidence: 99%
“…Such dependencies are interesting because while they exist across languages, they are nevertheless rare (Ferrer‐i Cancho, 2006; Straka, Hajic, Straková, & Hajic, 2015), and they help in understanding formal properties of natural languages (Joshi, 1985; Kuhlmann & Möhl, 2007; Shieber, 1985). More importantly, they are difficult for computational parsers (Gómez‐Rodríguez, Weir, & Carroll, 2009; Kübler et al, 2009; Kuhlmann & Satta, 2009; McDonald & Satta, 2007; Nederhof, 1999; Neuhaus & Bröker, 1997; Nivre, 2009; Pitler, Kannan, & Marcus, 2013; Vijay‐Shankar & Joshi, 1985), and they are known to pose difficulty for humans (Boland, Tanenhaus, Garnsey, & Carlson, 1995; Husain & Vasishth, 2015; Levy et al, 2012; Traxler & Pickering, 1996; Yadav, Vaidya, & Husain, 2017).…”
Section: Methodsmentioning
confidence: 99%
“…Unfortunately, exact inference has been shown to be intractable for models that support arbitrary non-projectivity, except under strong independence assumptions (McDonald and Satta 2007) which enable parsing in quadratic time with maximum spanning tree algorithms (McDonald et al 2005), but severely limit the expressivity of the feature models that can be used. This restriction can be avoided by using so-called mildly non-projective parsing algorithms, which support the overwhelming majority of non-projective analyses that can be found in real linguistic structures (Gómez-Rodríguez et al 2011; Cohen et al 2011;Pitler et al 2013); but they have supercubic complexities that make them too slow for practical use. Another option is to forgo exact inference, using approximate inference algorithms with rich feature models instead.…”
Section: Parsingmentioning
confidence: 99%
“…Our proof is very similar in style and structure to Pitler et al (2013). The general approach is to consider the set of structures an item could represent, and divide them into cases based on properties of the internal structure.…”
Section: Propertiesmentioning
confidence: 99%
“…Note that by using subsets of our rules, we can restrict the space of structures we generate, giving parsing algorithms for projective DAGs, projective trees (Eisner 1996), or 1-EC trees (Pitler et al 2013). Also, versions of these spaces with undirected edges could be easily handled with the same approach.…”
Section: Propertiesmentioning
confidence: 99%
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