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We study the submodular secretary problem with a cardinality constraint. Inthis problem, $n$ candidates for secretaries appear sequentially in randomorder. At the arrival of each candidate, a decision maker must irrevocablydecide 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$(\mathrm{e} - 1)^2 / (\mathrm{e}^2 (1 + \mathrm{e}))$-competitive algorithmfor this problem, which improves the best one known so far.

An improved algorithm for the submodular secretary problem with a cardinality constraint