2 Online Algorithms 2.1 Ski Rental Problem (rent-or-buy)

Online algorithms use a different model from what we’ve seen so far: the algorithm does not have the entire input at its beginning, but receives it piece by piece, sequentially, over time. After receiving each piece, the algorithm must immediately make a decision (updating a data structure, buying/selling stocks) which each have an associated cost. Ultimately, the goal of the algorithm is to minimize the total cost over time. Under this model, an offline algorithm is equivalent to receiving the entire input first, then making all decisions at the end with the full information. If we placed no restrictions on the ability to retract decisions (by making it expensive or disallowing it entirely), we could have our online algorithm perform a full recomputation after receiving each new piece of input, and obtain a solution equivalent to the offline version. There are various flavors of this restriction, some which are more domain-focused: