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Hidden Markov models (HMMs) and their variants were successfully used forseveral sequence annotation tasks. Traditionally, inference with HMMs is doneusing the Viterbi and posterior decoding algorithms. However, recently avariety of different optimization criteria and associated computationalproblems were proposed. In this paper, we consider three HMM decoding criteriaand prove their NP hardness. These criteria consider the set of states used togenerate a certain sequence, but abstract from the exact locations of regionsemitted by individual states. We also illustrate experimentally that thesecriteria are useful for HIV recombination detection.

Sequence Annotation with HMMs: New Problems and Their Complexity