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An Optimal Algorithm for the Distinct Elements Problem

Summary: First algorithm achieving information-theoretically optimal space O(ε^-2 + log n) bits for (1±ε)-approximate distinct elements in data streams, closing decades of work. Also attains worst-case O(1) update and reporting time and extends to Hamming-norm estimation. (summarized by gpt-5-mini on Feb 09 2026)

Paper ID
1505
Venue
PODS
Year
2010
Pagerank
0.00017772185
Overall Rank
482 | 96.70%
DOI
10.1145/1807085.1807094

Incoming Non-self Citations Over Time

Authors

BibTeX Citation

@inproceedings{kane_pods10,
        address = {New York, NY, USA},
        series = {{PODS} '10},
        title = {{An Optimal Algorithm for the Distinct Elements Problem}},
        url = {https://dl.acm.org/doi/10.1145/1807085.1807094},
        doi = {10.1145/1807085.1807094},
        booktitle = {Proceedings of the {ACM} {SIGMOD} Symposium on {Principles} of {Database} {Systems}},
        publisher = {Association for Computing Machinery},
        author = {Kane, Daniel M. and Nelson, Jelani and Woodruff, David P.},
        year = {2010}
}

Incoming Citations (Sorted by Pagerank)

Showing 32 of 32 citing papers.

Rank Citing Paper Year Venue Pagerank
451 Mergeable Summaries 2012 PODS 0.00018151445
777 Tight Bounds for Lp Samplers, Finding Duplicates in Streams, and Related Problems 2011 PODS 0.0001410593
1,146 Graph Sketches: Sparsification, Spanners, and Subgraphs 2012 PODS 0.00011984702
2,792 All-Distances Sketches, Revisited: HIP Estimators for Massive Graphs Analysis 2014 PODS 8.1191853e-05
2,992 Pan-private Algorithms Via Statistics on Sketches 2011 PODS 7.8836024e-05
3,795 Is Min-Wise Hashing Optimal for Summarizing Set Intersection? 2014 PODS 7.1200458e-05
4,291 A Framework for Adversarially Robust Streaming Algorithms 2020 PODS 6.7786745e-05
4,409 MNC: Structure-Exploiting Sparsity Estimation for Matrix Expressions 2019 SIGMOD 6.7178579e-05
4,971 Persistent Bloom Filter: Membership Testing for the Entire History 2018 SIGMOD 6.4195676e-05
5,255 At-the-time and Back-in-time Persistent Sketches 2021 SIGMOD 6.2982495e-05
5,669 Data Streams with Bounded Deletions 2018 PODS 6.1278944e-05
5,996 The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication 2015 PODS 6.0150613e-05
5,998 Approximate Distinct Counts for Billions of Datasets 2019 SIGMOD 6.0142553e-05
6,934 Better Cardinality Estimators for HyperLogLog, PCSA, and Beyond 2023 PODS 5.7351e-05
7,256 Weighted Distinct Sampling: Cardinality Estimation for SPJ Queries 2021 SIGMOD 5.6625146e-05
7,328 On the Feasibility of Forgetting in Data Streams 2024 PODS 5.6435171e-05
7,698 Tight Trade-offs for the Maximum k-Coverage Problem in the General Streaming Model 2019 PODS 5.5657914e-05
7,918 Subspace Exploration: Bounds on Projected Frequency Estimation 2021 PODS 5.5181056e-05
8,267 Streaming Algorithms for Measuring H-Impact 2017 PODS 5.4574671e-05
10,162 On Sketching Trimmed Statistics 2026 PODS 5.093636e-05
10,181 Representation Obliviousness and Pseudodeterminism in Streaming Algorithms 2026 PODS 5.093636e-05
10,310 A Fast, Mergeable, and LDP Compatible Sketch for Counting the Number of Distinct Values in Fully Dynamic Tables 2026 SIGMOD 5.093636e-05
10,651 Robust Statistical Analysis on Streaming Data with Near-Duplicates in General Metric Spaces 2025 PODS 5.093636e-05
11,374 Weighted Minwise Hashing Beats Linear Sketching for Inner Product Estimation 2023 PODS 5.093636e-05
11,375 Applications of Sketching and Pathways to Impact 2023 PODS 5.093636e-05
11,528 Estimation of the Size of Union of Delphic Sets: Achieving Independence from Stream Size 2022 PODS 5.093636e-05
11,631 Model Counting meets F0 Estimation 2021 PODS 5.093636e-05
11,640 Estimating the Size of Union of Sets in Streaming Models 2021 PODS 5.093636e-05
11,894 Distributed Statistical Estimation of Matrix Products with Applications 2018 PODS 5.093636e-05
11,897 Distinct Sampling on Streaming Data with Near-Duplicates 2018 PODS 5.093636e-05
11,899 Reconciling Graphs and Sets of Sets 2018 PODS 5.093636e-05
12,034 Streaming Algorithms for Robust Distinct Elements 2016 SIGMOD 5.093636e-05
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Outgoing Citations (Sorted by Pagerank)

Showing 8 of 8 cited papers.

Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.

Rank Cited Paper Year Venue Pagerank
1 Access Path Selection in a Relational Database Management System 1979 SIGMOD 0.0024089429
255 Distinct Sampling for Highly-Accurate Answers to Distinct Values Queries and Event Reports 2001 VLDB 0.00023174541
327 The Aqua Approximate Query Answering System 1999 SIGMOD 0.00021091539
432 Mining Database Structure; Or, How to Build a Data Quality Browser 2002 SIGMOD 0.00018572055
654 Storage Estimation for Multidimensional Aggregates in the Presence of Hierarchies 1996 VLDB 0.0001527187
689 On Synopses for Distinct-Value Estimation Under Multiset Operations 2007 SIGMOD 0.00014940023
2,197 Multi-Dimensional Clustering: A New Data Layout Scheme in DB2 2003 SIGMOD 8.9684812e-05
3,150 Comparing Data Streams Using Hamming Norms (How to Zero In) 2002 VLDB 7.7055991e-05
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