A lower-complexity Viterbi algorithm

In continuous speech recognition, when using statistical language models (e.g. bigrams) a significant amount of time is used every frame to evaluate interword transitions. In fact, if N is the size of vocabulary, O(N²) operations are required per frame. Also, when evaluating fully connected HMM with N states, the Viterbi algorithm requires O(N²) operations per frame. This paper presents the first algorithm to break the O(N²) complexity requirement in the Viterbi algorithm, whether evaluating interword transitions or evaluating a fully connected HMM. The algorithm presented has an average complexity of O(N√N). Previous speed-ups of the evaluations of interword transitions used heuristics, like pruning, or relied upon unavailability of many of the bigram values. However, this paper does not rely on any heuristics but fundamentally improves the basic evaluation of the time synchronous Viterbi algorithm