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We reformulate the problem of finding the sparsest representation of a given signal using an overcomplete dictionary as a bounded error subset selection problem. Specifically, the reconstructed signal is allowed to differ from the original signal by a bounded error. We argue that this bounded error formulation is natural in many applications, such as coding. Our novel formulation guarantees the sparsest solution to the bounded error subset selection problem by minimizing the number of nonzero coefficients in the solution vector. We show that this solution can be computed by finding the minimum cost flow path of an equivalent network. Integer programming is adopted to find the solution.