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# lecture21 - Lecture 21: Competitive Analysis Steven Skiena...

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Lecture 21: Competitive Analysis Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794–4400 http://www.cs.sunysb.edu/ skiena

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Motivation: Online Problems Many problems in both finance and computer science reduce to trying to predict the future. . . Examples from computer science include cache and virtual memory management. Examples from finance typically revolve around predicting future returns for an asset, or designing a portfolio to maximize future returns. Such problems become trivial if we know the future (i.e. the stream of future memory requests or tomorrow’s newspaper), but typically we only have access to the past.
On Line vs. Off Line An off-line problem provides access to all the relevant information to compute a result. An online problem continually produces new input and requires answers in response.

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Competitive Analysis How can we theoretically evaluate how well an algorithm forecasts the future? Statistical forecasts provide a predict the future that makes some sense in practice. However, they offer no future guarantees, particularly if the data distribution changes. Competitive analysis offers a worst-case measure of the quality of the behavior of an algorithm which predicts the future. We seek to compare the performance of algorithm A with only knowledge of the past with an algorithm which has complete knowledge of past and future makes optimal use of it.
We say an online algorithm ALG is c -competitive if there is a constant α such that for all finite input sequences I , ALG ( I ) c · OPT ( I ) + α Note that the additive constant α is a fixed cost that becomes unimportant as the size of the problem increases. We do not particularly care about the run-time efficiency of

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## This note was uploaded on 01/02/2012 for the course FINANCE 347 taught by Professor Bayou during the Fall '11 term at NYU.

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lecture21 - Lecture 21: Competitive Analysis Steven Skiena...

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