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This paper takes a first step towards generalizing compact routing to arbitrary routing policies that favor a broader set of path attributes beyond path length. Using the formalism of routing algebras we identify the algebraic requirements for a routing policy to be realizable with sublinear size routing tables and we show that a wealth of practical policies can be classified by our results. By generalizing the notion of stretch, we also discover the algebraic validity of compact routing schemes considered so far and we show that there are routing policies for which one cannot expect sublinear scaling even if permitting arbitrary constant stretch.