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The Viterbi algorithm is an efficient technique to estimate the state sequence of a discrete-time finite-state Markov process in the presence of memoryless noise. This work sets up a relationship to a general class of linear and nonlinear fast algorithms such as FFT, FWT, and optimal sorting. The performance of a Viterbi detector is a function of the minimum distance between signals in the observation space of the estimated Markov process. It is shown that this distance may efficiently be calculated with dynamic programming using a slightly modified Viterbi algorithm of an increased basis.