Instructor : Nikhil Bansal Scribe :
نویسنده
چکیده
In this lecture we will be looking into the secretary problem, and an interesting variation of the problem called the incentive comparable secretary problem. For both of these problems we will show how they can be solved though a correspondence between all possible strategies and the feasible solution space to a linear program. In both cases this will allow us to derive an algorithm and prove that it is the best algorithm for the problem. We will give an algorithm that is non-adaptive and must commit to box selection before moving on that achieves at least 18 of the reward of the best adaptive algorithm even when the adaptive algorithm can choose the best box after they are all opened. The methods for solving this problem will be similar to the secretary problem, showing a correspondence between strategies of opt and the feasible solution space of a linear program. We will then use the optimal solution of the linear program as a bound for opt and show that we are competitive with this bound.
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