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The Ski Rental Problem

ski rental problem is a classic example problem in online algorithms. It feels like a small but interesting problem that can be explained relatively easily while some clever tricks can be applied to it.

In this article, I took these lecture notes by Debmalya Panigrahi and Hangjie Ji and tried to rewrite them in a way that is easier to understand (at least for me). Assuming you wound know the number $k$ of days you will want to ski in advance, an optimal algorithm can be derived. This is probably not applicable in reality, however when one would do many decisions similar to this fictional scenario, the randomized algorithm could theoretically be a way to optimize the cost.

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