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DOI: 10.4230/LIPIcs.STACS.2008.1331
URN: urn:nbn:de:0030-drops-13313
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1331/
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Lotker, Zvi ; Patt-Shamir, Boaz ; Rawitz, Dror

Rent, Lease or Buy: Randomized Algorithms for Multislope Ski Rental

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Abstract

In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a one-time setup cost (``buying price''), and cost proportional to the duration of the usage (``rental rate''). The larger the price, the smaller the rent. The actual usage time is determined by an adversary, and the goal of an algorithm is to minimize the cost by choosing the best option at any point in time. Multislope Ski Rental is a natural generalization of the classical Ski Rental problem (where the only options are pure rent and pure buy), which is one of the fundamental problems of online computation. The Multislope Ski Rental problem is an abstraction of many problems where online decisions cannot be modeled by just two options, e.g., power management in systems which can be shut down in parts. In this paper we study randomized algorithms for Multislope Ski Rental. Our results include the best possible online randomized strategy for any additive instance, where the cost of switching from one option to another is the difference in their buying prices; and an algorithm that produces an $e$-competitive randomized strategy for any (non-additive) instance.

BibTeX - Entry

@InProceedings{lotker_et_al:LIPIcs:2008:1331,
  author =	{Zvi Lotker and Boaz Patt-Shamir and Dror Rawitz},
  title =	{{Rent, Lease or Buy: Randomized Algorithms for Multislope Ski Rental}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{503--514},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1331},
  URN =		{urn:nbn:de:0030-drops-13313},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2008.1331},
  annote =	{Keywords: Competitive analysis, ski rental, randomized algorithms}
}

Keywords: Competitive analysis, ski rental, randomized algorithms
Seminar: 25th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2008
Date of publication: 06.02.2008


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