Can entropy characterize performance of online algorithms?

Authors:
Gopal Pandurangan;Eli Upfal
Affiliations:
Computer Science Department, Brown University, Box 1910, Providence, RI;Computer Science Department, Brown University, Box 1910, Providence, RI
Venue:
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Year:
2001

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Abstract

We focus in this work on an aspect of online computation that is not addressed by the standard competitive analysis. Namely, identifying request sequences for which non-trivial online algorithms are useful versus request sequences for which all algorithms perform equally bad. The motivation for this work are advanced system and architecture designs which allow the operating system to dynamically allocate resources to online protocols such as prefetching and caching. To utilize these features the operating system needs to identify data streams that can benefit from more resources.Our approach in this work is based on the relation between entropy, compression and gambling, extensively studied in information theory. It has been shown that in some settings entropy can either fully or at least partially characterize the expected outcome of an iterative gambling game. Viewing online problem with stochastic input as an iterative gambling game, our goal is to study the extent to which the entropy of the input characterizes the expected performance of online algorithms for problems that arise in computer applications. We study bounds based on entropy for three online problems — list accessing, prefetching and caching. We show that entropy is a good performance characterizer for prefetching, but not so good characterizer for online caching.