Hidden Markov models (HMMs) have received considerable attention in various communities (e.g, speech recognition, neurology and bioinformatic) since many applications that use HMM have emerged. The goal of this work is to identify efficiently and correctly the model in a given dataset that yields the state sequence with the highest likelihood with respect to the query sequence. We propose SPIRAL, a fast search method for HMM datasets. To reduce the search cost, SPIRAL efficiently prunes a significant number of search candidates by applying successive approximations when estimating likelihood. SPIRAL is based on three ideas; (1) it clusters states of models to compute approximate likelihood, (2) it uses several granularities and approximate likelihood values in search processing, and (3) it focuses on just the promising likelihood computations by pruning out low-likelihood state sequences. We perform several experiments to verify the effectiveness of SPIRAL. The results show that SPIRA...