Finding the N best vertices in an infinite weighted hypergraph

Johanna Björklund, Frank Drewes, Anna Jonsson

Abstract: We propose an algorithm for computing the N best vertices in a weighted acyclic hypergraph over a nice semiring. A semiring is nice if it is finitely-generated, idempotent, and has 1<math><mn mathvariant="double-struck" is="true">1</mn></math> as its minimal element. We then apply the algorithm to the problem of computing the N best trees with respect to a weighted tree automaton, and complement theoretical correctness and complexity arguments with experimental data. The algorithm has several practical applications in natural language processing, for example, to derive the N most likely parse trees with respect to a probabilistic context-free grammar.