We explore various techniques to compress a permutation $\pi$ over $n$ integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi(i)$ and the application of its inverse $\pi^{-1}(i)$ 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 applications $\pi^{k}(i)$ of it, of integer functions, and of inverted lists and suffix arrays.
@InProceedings{barbay_et_al:LIPIcs.STACS.2009.1814, author = {Barbay, Jeremy and Navarro, Gonzalo}, title = {{Compressed Representations of Permutations, and Applications}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {111--122}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-09-5}, ISSN = {1868-8969}, year = {2009}, volume = {3}, editor = {Albers, Susanne and Marion, Jean-Yves}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1814}, URN = {urn:nbn:de:0030-drops-18148}, doi = {10.4230/LIPIcs.STACS.2009.1814}, annote = {Keywords: Compression, Permutations, Succinct data structures, Adaptive sorting} }
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