Rent, lease or buy: Randomized algorithms for multislope Ski rental

Zvi Lotker, Boaz Patt-Shamir, Dror Rawitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

37 Scopus citations

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.

Original languageEnglish
Title of host publicationProceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008
PublisherIBFI Schloss Dagstuhl
Pages503-514
Number of pages12
ISBN (Print)9783939897064
StatePublished - 1 Jan 2008
Event25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008 - Bordeaux, France
Duration: 21 Feb 200823 Feb 2008

Publication series

NameProceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008

Conference

Conference25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008
Country/TerritoryFrance
CityBordeaux
Period21/02/0823/02/08

Keywords

  • Competitive analysis
  • Randomized algorithms
  • Ski rental

ASJC Scopus subject areas

  • Computer Science (all)

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