On-line Viterbi Algorithm and Its Relationship to Random Walks

In this paper, we introduce the on-line Viterbi algorithm for decoding hidden Markov models (HMMs) in much smaller than linear space. Our analysis on two-state HMMs suggests that the expected maximum memory used to decode sequence of length n with m-state HMM can be as low as Θ(m log n), without a significant slow-down compared to the classical Viterbi algorithm. Classical Viterbi algorithm requires O(mn) space, which is impractical for analysis of long DNA sequences (such as complete human genome chromosomes) and for continuous data streams. We also experimentally demonstrate the performance of the on-line Viterbi algorithm on a simple HMM for gene finding on both simulated and real DNA sequences.