Departmental Papers (CIS)

Date of this Version

May 2001

Document Type

Conference Paper

Comments

Postprint version. Copyright ACM, 2001. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the 20th ACM Symposium on Principles of Database Systems (PODS), pages 171-182.
Publisher URL: http://doi.acm.org/10.1145/375551.375577

Abstract

We study the problem of computing a function f(x1, ..., xn) given that the actual values of the variables xi's are known only with some uncertainity. For each variable xi, an interval Ii is known such that the value of xi is guaranteed to fall within this interval. Any such interval can be probed to obtain the actual value of the underlying variable; however, there is a cost associated with each such probe. The goal is to adaptively identify a minimum cost sequence of probes such that regardless of the actual values taken by the unprobed xi's, the value of the function f can be computed to within a specified precision.

We design online algorithms for this problem when f is either the selection function or an aggregation function such as sum or average. We consider three natural models of precision and give algorithms for each model. We analyze our algorithms in the framework of competitive analysis and show that our algorithms are asymptotically optimal. Finally, we also study online algorithms for functions that are obtained by composing together selection and aggregation functions.

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Date Posted: 23 December 2005