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The submodular secretary problem

By Mohammadhossein Bateni, Mohammadtaghi Hajiaghayi and Morteza Zadimoghaddam


Online auction is an essence of many modern markets, particularly networked markets, in which information about goods, agents, and outcomes is revealed over a period of time, and the agents must make irrevocable decisions without knowing future information. Optimal stopping theory, especially the classic secretary problem, is a powerful tool for analyzing such online scenarios which generally require optimizing an objective function over the input. The secretary problem and its generalization the multiple-choice secretary problem were under a thorough study in the literature. In this paper, we consider a very general setting of the latter problem called the submodular secretary problem, in which the goal is to select k secretaries so as to maximize the expectation of a submodular function which defines efficiency of the selected secretarial group based on their overlapping skills. We present the first constant-competitive algorithm for this case. We consider some special cases of our general setting as well.

Year: 2009
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