Abstract
In a recent paper [MRL98], we had described a general framework for single pass approximate quantile finding algorithms. This framework included several known algorithms as special cases. We had identified a new algorithm, within the framework, which had a significantly smaller requirement for main memory than other known algorithms. In this paper, we address two issues left open in our earlier paper. First, all known and space efficient algorithms for approximate quantile finding require advance knowledge of the length of the input sequence. Many important database applications employing quantiles cannot provide this information. In this paper, we present a novel non-uniform random sampling scheme and an extension of our framework. Together, they form the basis of a new algorithm which computes approximate quantiles without knowing the input sequence length. Second, if the desired quantile is an extreme value (e.g., within the top 1% of the elements), the space requirements of currently known algorithms are overly pessimistic. We provide a simple algorithm which estimates extreme values using less space than required by the earlier more general technique for computing all quantiles. Our principal observation here is that random sampling is quantifiably better when estimating extreme values than is the case with the median.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.