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The main goal of this paper is to develop a new embedding method which we useto show that some finite metric spaces admit low-distortion embeddings into allnon-superreflexive spaces. This method is based on the theory ofequal-signs-additive sequences developed by Brunel and Sucheston (1975-1976).We also show that some of the low-distortion embeddability results obtainedusing this method cannot be obtained using the method based on thefactorization between the summing basis and the unit vector basis of $\ell_1$,which was used by Bourgain (1986) and Johnson and Schechtman (2009).

A new approach to low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces