The Online Specialization Problem

Abstract : We study the online specialization problem, where items arrive in an online fashion for processing by one of n different methods. Each method has two costs: a processing cost (paid once for each item processed), and a set-up cost (paid only once, on the method's first use). There are n possible types of items; an item's type determines the set of methods available to process it. Each method has a different degree of specialization. Highly specialized methods can process few item types while generic methods may process all item types. This is a generalization of ski-rental and closely related to the capital investment problem of Y. Azar, Y. Bartal, E. Feuerstein, A. Fiat, S. Leonardi, and A. Rosen. On capital investment. In Algorithmica, 25(1):22-36, 1999.. We primarily study the case where method i+1 is always more specialized than method i and the set-up cost for a more specialized method is always higher than that of a less specialized method. We describe an algorithm with competitive ratio O(log(n)), and also show an Ω (log(n)) lower bound on the competitive ratio for this problem; this shows our ratio is tight up to constant factors.
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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2006, 8, pp.97-120
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Edwin S. Hong. The Online Specialization Problem. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2006, 8, pp.97-120. 〈hal-00961104〉

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