An improved algorithm for the submodular secretary problem with a cardinality constraint
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We study the submodular secretary problem with a cardinality constraint. In this problem, n candidates for secretaries appear sequentially in random order. At the arrival of each candidate, a decision maker must irrevocably decide whether to hire him. The decision maker aims to hire at most k candidates that maximize a non-negative submodular set function. We propose an (e - 1)^2 / (e^2 (1 + e))-competitive algorithm for this problem, which improves the best one known so far.
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