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)
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Authors
- 1. Sepehr Assadi
- 2. Vihan Shah
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Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 331 | The Ubiquity of Large Graphs and Surprising Challenges of Graph Processing | 2018 | VLDB | 0.00027214222 |
| 392 | Counting Triangles in Data Streams | 2006 | PODS | 0.00024556183 |
| 4,953 | On Join Sampling and the Hardness of Combinatorial Output-Sensitive Join Algorithms | 2023 | PODS | 5.8085795e-05 |
| 5,046 | Better Algorithms for Counting Triangles in Data Streams | 2016 | PODS | 5.7405307e-05 |
| 5,104 | Guaranteeing the O~(AGM/OUT) Runtime for Uniform Sampling and Size Estimation over Joins | 2023 | PODS | 5.6946113e-05 |
| 6,468 | The Complexity of Counting Cycles in the Adjacency List Streaming Model | 2019 | PODS | 5.0526408e-05 |
| 6,864 | Triangle and Four Cycle Counting in the Data Stream Model | 2020 | PODS | 4.9050236e-05 |
| 7,065 | Fast Matrix Multiplication for Query Processing | 2024 | PODS | 4.8447515e-05 |
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