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An improved algorithm for the submodular secretary problem with a cardinality constraint (1905.04941v1)
Published 13 May 2019 in cs.DS
Abstract: 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 $(\mathrm{e} - 1)2 / (\mathrm{e}2 (1 + \mathrm{e}))$-competitive algorithm for this problem, which improves the best one known so far.