Parsing To 1-Endpoint-Crossing, Pagenumber-2 Graphs

We study the Maximum Subgraph problem in deep dependency parsing. We consider two restrictions to deep dependency graphs: (a) 1-endpoint-crossing and (b) pagenumber-2. Our main contribution is an exact algorithm that obtains maximum subgraphs satisfying both restrictions simultaneously in time O(n(5)). Moreover, ignoring one linguistically-rare structure descreases the complexity to O(n(4)). We also extend our quartic-time algorithm into a practical parser with a discriminative dis-ambiguation model and evaluate its performance on four linguistic data sets used in semantic dependency parsing.