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On compressing permutations and adaptive sorting

2013
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Theoretical Computer Science
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We prove that, given a permutation π over [1..n] formed of nRuns sorted blocks of sizes given by the vector R = r 1 , . . . , r nRuns , there exists a compressed data structure encoding n r i n(1 + log 2 nRuns) bits while supporting access to the values of π () and π −1 () in time O(log nRuns/ log log n) in the worst case and O(H(R)/ log log n) on average, when the argument is uniformly distributed over [1..n]. This data structure can be constructed in time O(n(1 + H(R))), which yields an

doi:10.1016/j.tcs.2013.10.019
fatcat:vxgaveeqkbhtdeuhbtfcczeery