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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
1506
Venue
PODS
Year
2010
Pagerank
0.00024820873
Overall Rank
383 | 97.34%
DOI
-

Incoming Non-self Citations Over Time

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Incoming Citations (Sorted by Pagerank)

Showing 27 of 27 citing papers.

Rank Citing Paper Year Venue Pagerank
402 Mergeable Summaries 2012 PODS 0.00024196343
1,040 Graph Sketches: Sparsification, Spanners, and Subgraphs 2012 PODS 0.00014488943
1,094 Tight Bounds for Lp Samplers, Finding Duplicates in Streams, and Related Problems 2011 PODS 0.00014129658
2,805 All-Distances Sketches, Revisited: HIP Estimators for Massive Graphs Analysis 2014 PODS 8.0918347e-05
2,894 Pan-private Algorithms Via Statistics on Sketches 2011 PODS 7.9474698e-05
3,708 Is Min-Wise Hashing Optimal for Summarizing Set Intersection? 2014 PODS 6.8247903e-05
4,403 A Framework for Adversarially Robust Streaming Algorithms 2020 PODS 6.2194225e-05
4,833 MNC: Structure-Exploiting Sparsity Estimation for Matrix Expressions 2019 SIGMOD 5.8916346e-05
5,332 Persistent Bloom Filter: Membership Testing for the Entire History 2018 SIGMOD 5.5662513e-05
5,902 The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication 2015 PODS 5.2796864e-05
5,909 At-the-time and Back-in-time Persistent Sketches 2021 SIGMOD 5.2769377e-05
6,244 Approximate Distinct Counts for Billions of Datasets 2019 SIGMOD 5.139669e-05
6,889 Better Cardinality Estimators for HyperLogLog, PCSA, and Beyond 2023 PODS 4.893581e-05
7,145 Tight Trade-offs for the Maximum k-Coverage Problem in the General Streaming Model 2019 PODS 4.8179617e-05
7,358 Weighted Distinct Sampling: Cardinality Estimation for SPJ Queries 2021 SIGMOD 4.7529363e-05
7,496 Subspace Exploration: Bounds on Projected Frequency Estimation 2021 PODS 4.7180617e-05
8,901 On the Feasibility of Forgetting in Data Streams 2024 PODS 4.427232e-05
10,008 Representation Obliviousness and Pseudodeterminism in Streaming Algorithms 2026 PODS 4.1945683e-05
10,012 A Fast, Mergeable, and LDP Compatible Sketch for Counting the Number of Distinct Values in Fully Dynamic Tables 2026 SIGMOD 4.1945683e-05
10,358 Robust Statistical Analysis on Streaming Data with Near-Duplicates in General Metric Spaces 2025 PODS 4.1945683e-05
11,168 Weighted Minwise Hashing Beats Linear Sketching for Inner Product Estimation 2023 PODS 4.1945683e-05
11,169 Applications of Sketching and Pathways to Impact 2023 PODS 4.1945683e-05
11,329 Estimation of the Size of Union of Delphic Sets: Achieving Independence from Stream Size 2022 PODS 4.1945683e-05
11,433 Model Counting meets F0 Estimation 2021 PODS 4.1945683e-05
11,442 Estimating the Size of Union of Sets in Streaming Models 2021 PODS 4.1945683e-05
11,765 Streaming Algorithms for Measuring H-Impact 2017 PODS 4.1945683e-05
11,833 Streaming Algorithms for Robust Distinct Elements 2016 SIGMOD 4.1945683e-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 0.0040449103
308 Distinct Sampling for Highly-Accurate Answers to Distinct Values Queries and Event Reports 2001 VLDB 0.00028142852
429 The Aqua Approximate Query Answering System 1999 SIGMOD 0.00023476494
475 Mining Database Structure; Or, How to Build a Data Quality Browser 2002 SIGMOD 0.00022303253
593 Storage Estimation for Multidimensional Aggregates in the Presence of Hierarchies 1996 VLDB 0.00019536993
727 On Synopses for Distinct-Value Estimation Under Multiset Operations 2007 SIGMOD 0.00017508726
2,045 Multi-Dimensional Clustering: A New Data Layout Scheme in DB2 2003 SIGMOD 9.6939983e-05
3,050 Comparing Data Streams Using Hamming Norms (How to Zero In) 2002 VLDB 7.6512619e-05
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