Abstract
We investigate the problem of succinctly representing an arbitrary permutation, π, on {0, . . ., n − 1} so that π k(i) can be computed quickly for any i and any (positive or negative integer) power k. A representation taking (1 + ∈)n lg n + O(1) bits suffices to compute arbitrary powers in constant time. A representation taking the optimal ⌈lg n!⌉ + o(n) bits can be used to compute arbitrary powers in O(lg n/lg lg n) time, or indeed in a minimal O(lg n) bit probes.
Work supported in part by UISTRF project 2001.04/IT
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Munro, J.I., Raman, R., Raman, V., Rao, S.S. (2003). Succinct Representations of Permutations. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_29
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DOI: https://doi.org/10.1007/3-540-45061-0_29
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