An Improved Fully Dynamic Algorithm for Counting 4-Cycles in General Graphs Using Fast Matrix Multiplication
Summary: Fully dynamic 4-cycle counting in general graphs; update time O(m^(2/3 − ε)) via fast matrix multiplication. Equivalence of layered and general graphs for counting; ω-based ε ≈ 0.0098 (ω=2.371) or 1/24 (ω=2) shows O(m^(2/3)) not tight, with a remaining Ω(m^(1/2−γ)) lower bound. (summarized by gpt-5-nano on Feb 09 2026)
Incoming Non-self Citations Over Time
Authors
- 1. Sepehr Assadi (University of Waterloo)
- 2. Vihan Shah (University of Waterloo)
BibTeX Citation
@inproceedings{assadi_pods25,
address = {New York, NY, USA},
series = {{PODS} '25},
title = {{An Improved Fully Dynamic Algorithm for Counting 4-Cycles in General Graphs Using Fast Matrix Multiplication}},
url = {https://dl.acm.org/doi/10.1145/3725228},
doi = {10.1145/3725228},
booktitle = {Proceedings of the {ACM} {SIGMOD} Symposium on {Principles} of {Database} {Systems}},
publisher = {Association for Computing Machinery},
author = {Assadi, Sepehr and Shah, Vihan},
year = {2025}
}Incoming Citations (Sorted by Pagerank)
Showing 1 of 1 citing papers.
| Rank | Citing Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 10,160 | Maintaining Queries under Updates Using Heavy-Light Partitioning of the Input Relations | 2026 | PODS | 5.093636e-05 |
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Outgoing Citations (Sorted by Pagerank)
Showing 9 of 9 cited papers.
Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 264 | The Ubiquity of Large Graphs and Surprising Challenges of Graph Processing | 2018 | VLDB | 0.00022980015 |
| 321 | Worst-Case Optimal Join Algorithms: Techniques, Results, and Open Problems | 2018 | PODS | 0.00021283186 |
| 458 | Counting Triangles in Data Streams | 2006 | PODS | 0.0001810876 |
| 3,453 | On Join Sampling and the Hardness of Combinatorial Output-Sensitive Join Algorithms | 2023 | PODS | 7.4004131e-05 |
| 3,941 | Guaranteeing the O~(AGM/OUT) Runtime for Uniform Sampling and Size Estimation over Joins | 2023 | PODS | 7.0074268e-05 |
| 5,110 | Better Algorithms for Counting Triangles in Data Streams | 2016 | PODS | 6.3609746e-05 |
| 6,363 | The Complexity of Counting Cycles in the Adjacency List Streaming Model | 2019 | PODS | 5.9000002e-05 |
| 6,873 | Triangle and Four Cycle Counting in the Data Stream Model | 2020 | PODS | 5.7495468e-05 |
| 6,885 | Fast Matrix Multiplication for Query Processing | 2024 | PODS | 5.7464502e-05 |
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