We formulate the problem of non-projective dependency parsing as a polynomial-sized integer linear program .

The model parameters are learned in a max-margin framework by employing a linear programming relaxation.

A linear program (LP) is an optimization problem of the form

If we add the constraint x E Zd, then the above is called an integer linear program (ILP).

Much attention has recently been devoted to integer linear programming (ILP) formulations of NLP problems, with interesting results in applications like semantic role labeling (Roth and Yih, 2005; Punyakanok et al., 2004), dependency parsing (Riedel and Clarke, 2006), word alignment for machine translation (Lacoste-Julien et al., 2006), summarization (Clarke and Lapata, 2008), and coreference resolution (Denis and Baldridge, 2007), among others.

We augment the standard perceptron algorithm with a global integer linear programming formulation to optimize both local fit of information into each topic and global coherence across the entire overview.

We estimate the parameters of our model using the perceptron algorithm augmented with an integer linear programming (ILP) formulation, run over a training set of example articles in the given domain.

To select the optimal excerpts, we employ integer linear programming (ILP).

Solving the ILP Solving an integer linear program is NP-hard (Cormen et al., 1992); however, in practice there exist several strategies for solving certain ILPs efficiently.

We combine this knowledge with discourse information, and formulate the debate side classification task as an Integer Linear Programming problem.

This information is employed, in conjunction with discourse information, in an Integer Linear Programming (ILP) framework.

We formulate the problem of finding the overall side of the post as an Integer Linear Programming (ILP) problem.