article

Deterministic sampling and range counting in geometric data streams

Authors:

Amitabha Bagchi,

Amitabh Chaudhary,

David Eppstein,

Michael T. GoodrichAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 3, Issue 2

Pages 16 - es

https://doi.org/10.1145/1240233.1240239

Published: 01 May 2007 Publication History

Abstract

We present memory-efficient deterministic algorithms for constructing ϵ-nets and ϵ-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are at least inverse-polylogarithmic. We also include a lower bound for noniceberg geometric queries.

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Index Terms

Deterministic sampling and range counting in geometric data streams
1. Mathematics of computing
  1. Probability and statistics
    1. Statistical paradigms
      1. Regression analysis
        Robust regression
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 3, Issue 2

May 2007

338 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1240233

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Copyright © 2007 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 2007

Published in TALG Volume 3, Issue 2

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Mathieu CRajaraman RYoung NYousefi AMarx D(2021)Competitive data-structure dynamizationProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458199(2269-2287)Online publication date: 10-Jan-2021
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https://doi.org/10.1109/IJCNN52387.2021.9533974
Shekelyan MDignos AGamper JGarofalakis M(2021)Approximating Multidimensional Range Counts with Maximum Error Guarantees2021 IEEE 37th International Conference on Data Engineering (ICDE)10.1109/ICDE51399.2021.00141(1595-1606)Online publication date: Apr-2021
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