Statistical MT has made great progress in the last few years, but current translation models are weak on re-ordering and target language fluency. Syntactic approaches seek to remedy these problems. In this paper, we take the framework for acquiring multi-level syntactic translation rules of (Galley et al., 2004) from aligned tree-string pairs, and present two main extensions of their approach: first, instead of merely computing a single derivation that minimally explains a sentence pair, we construct a large number of derivations that include contextually richer rules, and account for multiple interpretations of unaligned words. Second, we propose probability estimates and a training procedure for weighting these rules. We contrast different approaches on real examples, show that our estimates based on multiple derivations favor phrasal re-orderings that are linguistically better motivated, and establish that our larger rules provide a 3.63 BLEU point increase over minimal rules.

The critical resource that limits the application of best-first search is memory. We present a new class of best-first search algorithms that reduce the space complexity. The key idea is to store only the Open list of generated nodes, but not the Closed list of expanded nodes. The solution path can be recovered by a divide-and-conquer technique, either as a bidirectional or unidirectional search. For many problems, frontier search dramatically reduces the memory required by best-first search. We apply frontier search to breadth-first search of sliding-tile puzzles and the 4-peg Towers of Hanoi problem, Dijkstra's algorithm on a grid with random edge costs, and the A* algorithm on the Fifteen Puzzle, the four-peg Towers of Hanoi Problem, and optimal sequence alignment in computational biology.