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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
0.00022914472
Overall Rank
449 | 96.89%
DOI
-

Incoming Non-self Citations Over Time

Authors

Incoming Citations (Sorted by Pagerank)

Showing 27 of 27 citing papers.

Rank Citing Paper Year Venue Pagerank
398 Mergeable Summaries 2012 PODS 0.00024383201
922 Graph Sketches: Sparsification, Spanners, and Subgraphs 2012 PODS 0.00015254436
1,117 Tight Bounds for Lp Samplers, Finding Duplicates in Streams, and Related Problems 2011 PODS 0.0001386123
2,811 All-Distances Sketches, Revisited: HIP Estimators for Massive Graphs Analysis 2014 PODS 8.0840418e-05
2,900 Pan-private Algorithms Via Statistics on Sketches 2011 PODS 7.9455873e-05
3,713 Is Min-Wise Hashing Optimal for Summarizing Set Intersection? 2014 PODS 6.8182579e-05
4,399 A Framework for Adversarially Robust Streaming Algorithms 2020 PODS 6.2134435e-05
4,835 MNC: Structure-Exploiting Sparsity Estimation for Matrix Expressions 2019 SIGMOD 5.8861112e-05
5,338 Persistent Bloom Filter: Membership Testing for the Entire History 2018 SIGMOD 5.5608985e-05
5,905 The Communication Complexity of Distributed Set-Joins with Applications to Matrix Multiplication 2015 PODS 5.2746158e-05
5,910 At-the-time and Back-in-time Persistent Sketches 2021 SIGMOD 5.2718714e-05
6,243 Approximate Distinct Counts for Billions of Datasets 2019 SIGMOD 5.1348218e-05
6,893 Better Cardinality Estimators for HyperLogLog, PCSA, and Beyond 2023 PODS 4.8888853e-05
7,146 Tight Trade-offs for the Maximum k-Coverage Problem in the General Streaming Model 2019 PODS 4.8133378e-05
7,340 Weighted Distinct Sampling: Cardinality Estimation for SPJ Queries 2021 SIGMOD 4.7526052e-05
7,495 Subspace Exploration: Bounds on Projected Frequency Estimation 2021 PODS 4.7135369e-05
8,902 On the Feasibility of Forgetting in Data Streams 2024 PODS 4.4229886e-05
10,008 Representation Obliviousness and Pseudodeterminism in Streaming Algorithms 2026 PODS 4.1905499e-05
10,012 A Fast, Mergeable, and LDP Compatible Sketch for Counting the Number of Distinct Values in Fully Dynamic Tables 2026 SIGMOD 4.1905499e-05
10,370 Robust Statistical Analysis on Streaming Data with Near-Duplicates in General Metric Spaces 2025 PODS 4.1905499e-05
11,171 Weighted Minwise Hashing Beats Linear Sketching for Inner Product Estimation 2023 PODS 4.1905499e-05
11,172 Applications of Sketching and Pathways to Impact 2023 PODS 4.1905499e-05
11,331 Estimation of the Size of Union of Delphic Sets: Achieving Independence from Stream Size 2022 PODS 4.1905499e-05
11,436 Model Counting meets F0 Estimation 2021 PODS 4.1905499e-05
11,445 Estimating the Size of Union of Sets in Streaming Models 2021 PODS 4.1905499e-05
11,773 Streaming Algorithms for Measuring H-Impact 2017 PODS 4.1905499e-05
11,841 Streaming Algorithms for Robust Distinct Elements 2016 SIGMOD 4.1905499e-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 0.0040465394
316 Distinct Sampling for Highly-Accurate Answers to Distinct Values Queries and Event Reports 2001 VLDB 0.00027981848
431 The Aqua Approximate Query Answering System 1999 SIGMOD 0.00023397171
481 Mining Database Structure; Or, How to Build a Data Quality Browser 2002 SIGMOD 0.000221538
600 Storage Estimation for Multidimensional Aggregates in the Presence of Hierarchies 1996 VLDB 0.00019400653
737 On Synopses for Distinct-Value Estimation Under Multiset Operations 2007 SIGMOD 0.00017377393
2,092 Multi-Dimensional Clustering: A New Data Layout Scheme in DB2 2003 SIGMOD 9.5635999e-05
3,123 Comparing Data Streams Using Hamming Norms (How to Zero In) 2002 VLDB 7.5270618e-05
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