Abstract
Recently, there has been renewed interest in semantic dependency parsing, among which one of the paradigms focuses on parsing directed acyclic graphs (DAGs). Consideration of the decoding problem in natural language semantic dependency parsing as finding a maximum spanning DAG of a weighted directed graph carries many complexities. In particular, the computational complexity (and approximability) of the problem has not been addressed in the literature to date. This paper helps to fill this gap, showing that this general problem is APX-hard, and is NP-hard even under the planar restriction, in the graphtheoretic sense. On the other hand, we show that under the restriction of projectivity, the problem has a straightforward O(n 3 ) algorithm. We also give some empirical evidence of the algorithmic importance of these graph restrictions, on data from the SemEval 2014 task 8 on Broad Coverage Semantic Dependency Parsing.
Highlights
Consideration of the decoding problem in natural language semantic dependency parsing as finding a maximum spanning directed acyclic graphs (DAGs) of a weighted directed graph carries many complexities that have not been addressed in the literature to date
We explain the APX-hardness of maximum spanning directed acyclic graph problem (MSDAG), by relating it to the almost identical minimum weighted feedback arc set and maximum weighted acyclic subgraph problems
Unlike in syntactic dependency parse decoding, where projective decoding given by Eisner (1996)’s algorithm has a slightly higher computational complexity (O(n3)) than the nonprojective (Tarjan) maximum spanning tree algorithm (O(n2)) (Tarjan, 1977; Chu and Liu, 1965; Edmonds, 1967; McDonald et al, 2005), finding the maximum spanning projective dependency DAG is tractable and can be found in time O(n3), contrary to its APX-hard non-projective counterpart
Summary
Consideration of the decoding problem in natural language semantic dependency parsing as finding a maximum spanning DAG of a weighted directed graph carries many complexities that have not been addressed in the literature to date. If there are no edge cuts in the graph consisting only of negative weighted edges, the 6 The NP-hardness of finding a planar or MSDAG and MWDAS solutions are identical.
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