Smooth representation of rankings

Abstract

An encoding of data for digital storage is called smooth, if, for any small change in the raw data, only a proportionately small change has to be made in the encoded data. In this paper, we consider the problem of smooth encoding for ordinal data, i.e., ranking of objects. It is shown that, simple efficient smooth encoding for storage (as well as compression) of rankings is possible with respect to the well-known Kendall τ metric on permutations.