We show that the decoding problem in generalized Higher Order Conditional Random Fields (CRFs) can be decomposed into two parts: one is a tree labeling problem that can be solved in linear time using dynamic programming; the other is a supermodular quadratic pseudo-Boolean maximization problem, which can be solved in cubic time using a minimum cut algorithm. We use dual decomposition to force their agreement. Experimental results on Twitter named entity recognition and sentence dependency tagging tasks show that our method outperforms spanning tree based dual decomposition.

Graph based dependency parsing is inefficient when handling non-local features due to high computational complexity of inference. In this paper, we proposed an exact and efficient decoding algorithm based on the Branch and Bound (B&B) framework where non-local features are bounded by a linear combination of local features. Dynamic programming is used to search the upper bound. Experiments are conducted on English PTB and Chinese CTB datasets. We achieved competitive Unlabeled Attachment Score (UAS) when no additional resources are available: 93.17% for English and 87.25% for Chinese. Parsing speed is 177 words per second for English and 97 words per second for Chinese. Our algorithm is general and can be adapted to non-projective dependency parsing or other graphical models.