We study the rate-distortion relationship in the set
of permutations endowed with the Kendall t-metric and the
Chebyshev metric. Our study is motivated by the application of permutation rate-distortion to the average-case and worst-case analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall t-metric we provide bounds for small, medium, and large distortion regimes, while for the Chebyshev metric we present bounds that are valid for all distortions and are especially accurate for small
distortions. In addition, for the Chebyshev metric, we provide a construction for covering codes
