A k-secretary algorithm achieving the optimal 1-O(1/sqrt(k)) competitive ratio with O(log k) memory via a reduction to a new O(log k)-memory quantile estimator with O(sqrt(k)) expected rank error.
Improved competitive ratio for the matroid secretary problem
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Optimal $k$-Secretary with Logarithmic Memory
A k-secretary algorithm achieving the optimal 1-O(1/sqrt(k)) competitive ratio with O(log k) memory via a reduction to a new O(log k)-memory quantile estimator with O(sqrt(k)) expected rank error.