Rastislav Sramek, Brona Brejova, Tomas Vinar. On-line Viterbi Algorithm and Its Relationship to Random Walks. Technical Report 0704.0062v1, arXiv, March 2007.

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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 \$Theta(mlog 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.