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<Paper uid="P06-2066">
  <Title>Mildly Non-Projective Dependency Structures</Title>
  <Section position="3" start_page="0" end_page="507" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Dependency-based representations have become increasingly popular in syntactic parsing, especially for languages that exhibit free or flexible word order, such as Czech (Collins et al., 1999), Bulgarian (Marinov and Nivre, 2005), and Turkish (EryiVgit and Oflazer, 2006). Many practical implementations of dependency parsing are restricted to projective structures, where the projection of a head word has to form a continuous substring of the sentence. While this constraint guarantees good parsing complexity, it is well-known that certain syntactic constructions can only be adequately represented by non-projective dependency structures, where the projection of a head can be discontinuous. This is especially relevant for languages with free or flexible word order.</Paragraph>
    <Paragraph position="1"> However, recent results in non-projective dependency parsing, especially using data-driven methods, indicate that most non-projective structures required for the analysis of natural language are very nearly projective, differing only minimally from the best projective approximation (Nivre and Nilsson, 2005; Hall and Novak, 2005; McDonald and Pereira, 2006). This raises the question of whether it is possible to characterize a class of mildly non-projective dependency structures that is rich enough to account for naturally occurring syntactic constructions, yet restricted enough to enable efficient parsing.</Paragraph>
    <Paragraph position="2"> In this paper, we review a number of proposals for classes of dependency structures that lie between strictly projective and completely unrestricted non-projective structures. These classes have in common that they can be characterized in terms of properties of the dependency structures themselves, rather than in terms of grammar formalisms that generate the structures. We compare the proposals from a theoretical point of view, and evaluate a subset of them empirically by testing their representational adequacy with respect to two dependency treebanks: the Prague Dependency Treebank (PDT) (HajiVc et al., 2001), and the Danish Dependency Treebank (DDT) (Kromann, 2003).</Paragraph>
    <Paragraph position="3"> The rest of the paper is structured as follows.</Paragraph>
    <Paragraph position="4"> In section 2, we provide a formal definition of dependency structures as a special kind of directed graphs, and characterize the notion of projectivity.</Paragraph>
    <Paragraph position="5"> In section 3, we define and compare five different constraints on mildly non-projective dependency structures that can be found in the literature: planarity, multiplanarity, well-nestedness, gap degree, and edge degree. In section 4, we provide an experimental evaluation of the notions of planarity, well-nestedness, gap degree, and edge degree, by  investigating how large a proportion of the dependency structures found in PDT and DDT are allowed under the different constraints. In section 5, we present our conclusions and suggestions for further research.</Paragraph>
  </Section>
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