2016/07/14 by Artūrs Bačkurs, Backurs, Arturs, Christos Tzamos +1 · 2 citations
Computer Science · #Algorithms and Data Compression #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning and Algorithms #Network Packet Processing and Optimization
paper · pdf · doi:10.48550/arxiv.1607.04229
openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations. It runs in time O(Tn2) given a sequence of T observations from a HMM with n states. Despite significant interest in the problem and prolonged effort by different communities, no known algorithm achieves more than a polylogarithmic speedup. In this paper, we explain this difficulty by providing matching conditional lower bounds. We show that the Viterbi algorithm runtime is optimal up to subpolynomial factors even when the number of distinct observations is small. Our lower bounds are based on assumptions that the best known algorithms for the All-Pairs Shortest Paths problem (APSP) and for the Max-Weight k-Clique problem in edge-weighted graphs are essentially tight. Finally, using a recent algorithm by Green Larsen and Williams for online Boolean matrix-vector multiplication, we get a 2^Ω(√ log n) speedup for the Viterbi algorithm when there are few distinct transition probabilities in the HMM.