Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutationover n integers, taking advantage of ordered subsequences in �, while supporting its application �(i) and the application of its inverse � −1 (i) in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applicationsk (i) of it, of integer functions, and of inverted lists and suffix arrays.

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