Estimating Sum by Weighted Sampling

  • Rajeev Motwani
  • Rina Panigrahy
  • Ying Xu
Conference paper

DOI: 10.1007/978-3-540-73420-8_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)
Cite this paper as:
Motwani R., Panigrahy R., Xu Y. (2007) Estimating Sum by Weighted Sampling. In: Arge L., Cachin C., Jurdziński T., Tarlecki A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg

Abstract

We study the classic problem of estimating the sum of n variables. The traditional uniform sampling approach requires a linear number of samples to provide any non-trivial guarantees on the estimated sum. In this paper we consider various sampling methods besides uniform sampling, in particular sampling a variable with probability proportional to its value, referred to as linear weighted sampling. If only linear weighted sampling is allowed, we show an algorithm for estimating sum with \(\tilde{O}(\sqrt n)\) samples, and it is almost optimal in the sense that \(\Omega(\sqrt n)\) samples are necessary for any reasonable sum estimator. If both uniform sampling and linear weighted sampling are allowed, we show a sum estimator with \(\tilde{O}(\sqrt[3]n)\) samples. More generally, we may allow general weighted sampling where the probability of sampling a variable is proportional to any function of its value. We prove a lower bound of \(\Omega(\sqrt[3]n)\) samples for any reasonable sum estimator using general weighted sampling, which implies that our algorithm combining uniform and linear weighted sampling is an almost optimal sum estimator.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Rajeev Motwani
    • 1
  • Rina Panigrahy
    • 2
  • Ying Xu
    • 1
  1. 1.Dept of Computer Science, Stanford UniversityUSA
  2. 2.Microsoft Research, Mountain View, CAUSA

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