On Finding the $K$-best Non-projective Dependency Trees

TL;DR

This paper extends the $K$-best dependency tree algorithm to handle root constraints, improving decoding efficiency and addressing the increased root violation rate when considering multiple top trees.

Contribution

It simplifies the $K$-best spanning tree algorithm and introduces a new method for decoding the top $K$ dependency trees with root constraints.

Findings

Achieved a constant time speed-up over the original algorithm.

Demonstrated increased root constraint violations with higher $K$ values.

Extended the $K$-best algorithm to include root constraints in dependency parsing.

Abstract

The connection between the maximum spanning tree in a directed graph and the best dependency tree of a sentence has been exploited by the NLP community. However, for many dependency parsing schemes, an important detail of this approach is that the spanning tree must have exactly one edge emanating from the root. While work has been done to efficiently solve this problem for finding the one-best dependency tree, no research has attempted to extend this solution to finding the $K$-best dependency trees. This is arguably a more important extension as a larger proportion of decoded trees will not be subject to the root constraint of dependency trees. Indeed, we show that the rate of root constraint violations increases by an average of $13$ times when decoding with $K\!=\!50$ as opposed to $K\!=\!1$. In this paper, we provide a simplification of the $K$-best spanning tree algorithm of Camerini et al. (1980). Our simplification allows us to obtain a constant time speed-up over the original algorithm. Furthermore, we present a novel extension of the algorithm for decoding the $K$-best dependency trees of a graph which are subject to a root constraint.