There are provided a method and a system for computation of optimal distance bounds on compressed time-series data. In a method for similarity search, the method includes the step of transforming sequence data into a compressed sequence represented by top-k coefficients of the sequence data and a sum of the energy of omitted coefficients of the sequence data. The method further includes the step of computing at least one of a lower bound and an upper bound on a distance range between a query sequence and the compressed sequence, given a first and a second constraint. The first constraint is that a sum of squares of the omitted coefficients is less than a sum of the energy of the omitted coefficients. The second constraint is that the energy of the omitted coefficients is less than the energy of a lowest energy one of the top-k coefficients.