Index Terms
Ski-rental problem , Competitive algorithms , Deterministic and randomized algorithms , On-line algorithms
Keywords and Synonyms
Oblivious adversaries , Worst-case approximation , Metrical task systems
Problem Definition
The ski rental problem was developed as a pedagogical tool for understanding the basic concepts in some early results in on-line algorithms.Footnote 1 The ski rental problem considers the plight of one consumer who, in order to socialize with peers, is forced to engage in a variety of athletic activities, such as skiing, bicycling, windsurfing, rollerblading, sky diving, scuba-diving, tennis, soccer, and ultimate Frisbee, each of which has a set of associated apparatus, clothing, or protective gear.
In all of these, it is possible either to purchase the accoutrements needed, or to rent them. For the purpose of this problem, it is assumed that one-time rental is less expensive than purchasing. It is also assumed that purchased items are durable, and suitable...
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- 1.
In the interest of full disclosure, the earliest presentations of these results described the problem as the wedding‐tuxedo‐rental problem. Objections were presented that this was a gender‐biased name for the problem, since while groomsmen can rent their wedding apparel, bridesmaids usually cannot. A further complication, owing to the difficulty of instantaneously producing fitted garments or ski equipment outlined below, suggests that some complications could have been avoided by focusing on the dilemma of choosing between daily lift passes or season passes, although this leads to the pricing complexities of purchasing season passes well in advance of the season, as opposed to the higher cost of purchasing them at the mountain during the ski season. A similar problem could be derived from the question as to whether to purchase the daily newspaper at a newsstand or to take a subscription, after adding the challenge that one's peers will treat one contemptuously if one has not read the news on days on which they have.
Recommended Reading
Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive Snoopy Caching. Algorithmica 3, 77–119 (1988) (Conference version: FOCS 1986, pp. 244–254)
Karlin, A.R., Manasse, M.S., McGeoch, L.A., Owicki, S.S.: Competitive Randomized Algorithms for Nonuniform Problems. Algorithmica 11(6), 542–571 (1994) (Conference version: SODA 1990, pp. 301–309)
Reingold, N., Westbrook, J., Sleator, D.D.: Randomized Competitive Algorithms for the List Update Problem. Algorithmica 11(1), 15–32 (1994) (Conference version included author Irani, S.: SODA 1991, pp. 251–260)
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© 2008 Springer-Verlag
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Manasse, M. (2008). Ski Rental Problem. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_378
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DOI: https://doi.org/10.1007/978-0-387-30162-4_378
Publisher Name: Springer, Boston, MA
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