# On-line Viterbi Algorithm and Its Relationship to Random Walks

## TL;DR

This paper presents an on-line Viterbi algorithm that significantly reduces memory usage for decoding hidden Markov models, enabling analysis of long sequences and streams with minimal slowdown.

## Contribution

The paper introduces a space-efficient on-line Viterbi algorithm and analyzes its expected memory usage, demonstrating practical advantages over the classical approach.

## Key findings

- Expected maximum memory is $ heta(m\log n)$ for two-state HMMs.
- Classical Viterbi requires $O(mn)$ space, which is impractical for long sequences.
- Experimental results show effective gene finding on DNA sequences.

## Abstract

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 $\Theta(m\log n)$, 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.