The parking permit problem

@article{Meyerson2005ThePP,
  title={The parking permit problem},
  author={Adam Meyerson},
  journal={46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)},
  year={2005},
  pages={274-282}
}
We consider online problems where purchases have time durations which expire regardless of whether the purchase is used or not. The parking permit problem is the natural analog of the well-studied ski rental problem in this model, and we provide matching upper and lower bounds on the competitive ratio for this problem. By extending the techniques thus developed, we give an online-competitive algorithm for the problem of renting steiner forest edges with time durations. 

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