An in-place, subquadratic algorithm for permutation inversion
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We assume the permutation π is given by an n-element array in which the i-th element denotes the value π(i). Constructing its inverse in-place (i.e. using O(n) bits of additional memory) can be achieved in linear time with a simple algorithm. Limiting the numbers that can be stored in our array to the range [1...n] still allows a straightforward O(n^2) time solution. The time complexity can be improved using randomization, but this only improves the expected, not the pessimistic running time. We present a deterministic algorithm that runs in O(n^3/2) time.
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