This dissertation is about ordering. The problem of arranging a set of n items in a desired order is quite common, as well as fundamental to computer science. Sorting is one instance, as is the Traveling Salesman Problem. Each problem instance can be thought of as optimization of a function that applies to the set of permutations.

The dissertation treats word reordering for machine translation as another instance of a combinatorial optimization problem. The approach introduced is to combine three different functions of permutations. The first function is based on finite-state automata, the second is an instance of the Linear Ordering Problem, and the third is an entirely new permutation problem related to the LOP.

The Linear Ordering Problem has the most attractive computational properties of the three, all of which are NP-hard optimization problems. The dissertation expends significant effort developing neighborhoods for local search on the LOP, and uses grammars and other tools from natural language parsing to introduce several new results, including a state-of-the-art local search procedure.

Combinatorial optimization problems such as the TSP or the LOP are usually given the function over permutations. In the machine translation setting, the weights are not given, only words. The dissertation applies machine learning techniques to derive a LOP from each given sentence using a corpus of sentences and their translations for training. It proposes a set of features for such learning and argues their propriety for translation based on an analogy to dependency parsing. It adapts a number of parameter optimization procedures to the novel setting of the LOP.

The signature result of the thesis is the application of a machine learned set of linear ordering problems to machine translation. Using reorderings found by search as a preprocessing step significantly improves translation of German to English, and significantly more than the lexicalized reordering model that is the default of the translation system.

In addition, the dissertation provides a number of new theoretical results, and lays out an ambitious program for potential future research. Both the reordering model and the optimization techniques have broad applicability, and the availability of machine learning makes even new problems without obvious structure approachable.