## An Efficient Algorithm for the n-Best-Strings Problem (2002)

Venue: | In Proceedings of the International Conference on Spoken Language Processing 2002 (ICSLP ’02 |

Citations: | 17 - 1 self |

### BibTeX

@INPROCEEDINGS{Mohri02anefficient,

author = {Mehryar Mohri and Michael Riley},

title = {An Efficient Algorithm for the n-Best-Strings Problem},

booktitle = {In Proceedings of the International Conference on Spoken Language Processing 2002 (ICSLP ’02},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

problem in a weighted automaton. This problem arises commonly in speech recognition applications when a ranked list of unique recognizer hypotheses is desired. We believe this is the first n-best algorithm to remove redundant hypotheses before rather than after the n-best determination. We give a detailed description of the algorithm and demonstrate its correctness. We report experimental results showing its efficiency and practicality even for large n in a 40; 000-word vocabulary North American Business News (NAB) task. In particular, we show that 1000-best generation in this task requires negligible added time over recognizer lattice generation.

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Citation Context ...the potentially exponential enumeration of redundant hypotheses. Our method is based on two general algorithms, the determinization of weighted automata [5, 6] and a general n-shortestpaths algorithm =-=[7]-=-. We use weighted determinization to deal with hypothesis redundancy -- several paths labeled with the same string -- and a single-source shortest paths algorithm to find the n strings with the lowest... |

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Citation Context ...search, but prior to it. In this way, we avoid the potentially exponential enumeration of redundant hypotheses. Our method is based on two general algorithms, the determinization of weighted automata =-=[5, 6]-=- and a general n-shortestpaths algorithm [7]. We use weighted determinization to deal with hypothesis redundancy -- several paths labeled with the same string -- and a single-source shortest paths alg... |

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Citation Context ... variants such as finding just the n shortest paths with no cycle, or the n shortest paths with distinct weights, which have all been studied extensively as well. An efficient algorithm introduced by =-=[2]-=- finds an implicit representation of the n shortest paths (allowing cycles and multiple edges) between two nodes in O(jEj + jQj log jQj + n), in constant time per path, after a preprocessing stage dom... |

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Citation Context ...neral and applies to all weighted automata. A weighted automaton is a directed weighted graph in which each edge or transition has a label -- a phoneme or a word in the case of phone or word lattices =-=[9, 10, 11, 12]-=-. The weights are often interpreted as negative log of probabilities, but in general they may correspond to some other measured quantity. They are added along each path and the weight of a string x is... |

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Citation Context ...speech recognition applications essentially consist of first determining the k shortest paths with k >> n and then of looking for the n distinct best strings out of the labels of the k paths obtained =-=[3, 4]-=-. This means that a very large number of hypotheses may be generated, compared to previous hypotheses, and then discarded because they are not distinct. We present an efficient algorithm for solving t... |

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Citation Context ...speech recognition applications essentially consist of first determining the k shortest paths with k >> n and then of looking for the n distinct best strings out of the labels of the k paths obtained =-=[3, 4]-=-. This means that a very large number of hypotheses may be generated, compared to previous hypotheses, and then discarded because they are not distinct. We present an efficient algorithm for solving t... |

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Citation Context ...inal state of B has been extracted from S n times (lines 7). Since at most n shortest paths may go through any state p, the search can be limited to at most n extraction of any state p (line 8). 1 In =-=[16]-=-, we also present a simple n-shortest-distance algorithm based on an n-tropical semiring and a generalized shortest-first priority queue. 1 1 1 1 1 1 NAB 40K Bigram 1. 1-Best 2. 10-Best 3. 100-Best 4.... |

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Citation Context ...We then apply the n-best algorithm in a separate step to this automaton. Since lattices with low lattice word error rates can be generated with very little added computation over one-best recognition =-=[8]-=-, this approach allows us to completely decouple the nbest generation from the first-pass recognition step with negligible cost in accuracy or efficiency. We describe our algorithm in detail and repor... |

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Citation Context ...search, but prior to it. In this way, we avoid the potentially exponential enumeration of redundant hypotheses. Our method is based on two general algorithms, the determinization of weighted automata =-=[5, 6]-=- and a general n-shortestpaths algorithm [7]. We use weighted determinization to deal with hypothesis redundancy -- several paths labeled with the same string -- and a single-source shortest paths alg... |

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Citation Context ...negligible added time over recognizer lattice generation. 1. MOTIVATION The problem of determining the n shortest paths of a weighted directed graph is a well-studied problem in computer science (see =-=[1]-=- for an extensive bibliography). The problem also admits a number of variants such as finding just the n shortest paths with no cycle, or the n shortest paths with distinct weights, which have all bee... |

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Allauzen and Mehryar Mohri, "On the Determinizability of Weighted Automata and Transducers
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Citation Context ...ure 1. Unlike the unweighted case, not all weighted automata are determinizable. There exists however a general characterization property and an efficient testing algorithm for checking that property =-=[5, 14]-=-. In particular, any acyclic weighted automaton is determinizable. This guarantees the termination of determinization 0 1 a/0.1 b/0.3 2 a/0.2 a/0.4 b/0.1 b/0.4 3/0 c/0.5 d/0.2 c/0.3 d/0.2 Fig. 1. Non-... |