A lot of work has gone into developing powerful optimization methods for solving these combinatorial problems.
we explore, analyze, and demonstrate that a substantially simpler randomized greedy inference algorithm already suffices for near optimal parsing: a) we analytically quantify the number of local optima that the greedy method has to overcome in the context of first-order parsing; b) we show that, as a decoding algorithm, the greedy method surpasses dual decomposition in second-order parsing; c) we empirically demonstrate that our approach with up to third-order and global features outperforms the state-of-the-art dual decomposition and MCMC sampling methods when evaluated on 14 languages of non-projective CoNLL datasets.