In a general framework where the concepts of subdominant/updominated play a crucial role, we give a vast overview of approximations with the supremum norm for many structures of classi-fication: (partial or nonpartial) ultrametrics,k-ultrametrics, convex and isotonic regressions. For tree semi-distances/dissimilarities and Robinsonian dissimilarities, we show how the general approach leads us to algorithms with a constant factor.