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The proliferation of biological sequence data has motivated the need for an extremely fast probabilistic sequence search. One method for performing this search involves evaluating the Viterbi probability of a hidden Markov model (HMM) of a desired sequence family for each sequence in a protein database. However, one of the difficulties with current implementations is the time required to search large databases. Many current and upcoming architectures offering large amounts of compute power are designed with data-parallel execution and streaming in mind. We present a streaming algorithm for evaluating an HMMs Viterbi probability and refine it for the specific HMM used in biological sequence search. We implement our streaming algorithm in the Brook language, allowing us to execute the algorithm on graphics processors. We demonstrate that this streaming algorithm on graphics processors can outperform available CPU implementations. We also demonstrate this implementation running on a 16 node graphics cluster.