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.
Highlights
To motivate the online specialization problem, consider the scenario of hosting an online data archival service
MLSA often creates the same specializations as ESA running on a related ES problem
A worker’s job is to process the inputs whose specialization level is inside its interval
Summary
To motivate the online specialization problem, consider the scenario of hosting an online data archival service. Customers are expected to store many data files into the archive regularly but rarely read data from the archive. To minimize the cost of operating the archive, the host could automatically compress the data files before storing them in archive. Since the incoming files could represent text, sound, or any number of other possible types, different compression algorithms are needed for an efficient system. Suppose there are four different methods for processing data: method f1 denoting no compression at all, f2 denoting a standard dictionary coding technique good for generic unicode text, f3 denoting a specialized encoding scheme for English prose, and f4 an efficient compressor for sound. We know f1 ≺ f2, f1 ≺ f4, and f2 is incomparable to f4
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