On maximum spanning DAG algorithms for semantic DAG parsing

Consideration of the decoding problem in semantic parsing as finding a maximum spanning DAG of a weighted directed graph carries many complexities that haven’t been fully addressed in the literature to date, among which are its actual appropriateness for the decoding task in semantic parsing, not to mention an explicit proof of its complexity (and its approximability). In this paper, we consider the objective function for the maximum spanning DAG problem, and what it means in terms of decoding for semantic parsing. In doing so, we give anecdotal evidence against its use in this task. In addition, we consider the only graph-based maximum spanning DAG approximation algorithm presented in the literature (without any approximation guarantee) to date and finally provide an approximation guarantee for it, showing that it is an O( 1 n) factor approximation algorithm, where n is the size of the digraph’s vertex set.