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
No non-self incoming citations found for this paper in this database.
Authors
- 1. Sepehr Assadi
- 2. Vihan Shah
Incoming Citations (Sorted by Pagerank)
Showing 0 of 0 citing papers.
| Rank | Citing Paper | Year | Venue | Pagerank |
|---|
Previous
Page 1 / 1
Next
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 |
|---|---|---|---|---|
| 267 | The Ubiquity of Large Graphs and Surprising Challenges of Graph Processing | 2018 | VLDB | 0.00023020464 |
| 454 | Counting Triangles in Data Streams | 2006 | PODS | 0.00018243292 |
| 4,293 | On Join Sampling and the Hardness of Combinatorial Output-Sensitive Join Algorithms | 2023 | PODS | 6.8490255e-05 |
| 4,463 | Guaranteeing the O~(AGM/OUT) Runtime for Uniform Sampling and Size Estimation over Joins | 2023 | PODS | 6.7462588e-05 |
| 4,930 | Better Algorithms for Counting Triangles in Data Streams | 2016 | PODS | 6.5040855e-05 |
| 6,236 | The Complexity of Counting Cycles in the Adjacency List Streaming Model | 2019 | PODS | 6.0070757e-05 |
| 6,619 | Triangle and Four Cycle Counting in the Data Stream Model | 2020 | PODS | 5.8801548e-05 |
| 6,806 | Fast Matrix Multiplication for Query Processing | 2024 | PODS | 5.8280405e-05 |
Previous
Page 1 / 1
Next
Semantically Similar Papers
| Overall Rank | Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 8,117 | Fast Local Subgraph Counting | 2024 | VLDB | 5.5419908e-05 |
| 454 | Counting Triangles in Data Streams | 2006 | PODS | 0.00018243292 |
| 4,453 | Approximately Counting Triangles in Large Graph Streams Including Edge Duplicates with a Fixed Memory Usage | 2018 | VLDB | 6.7506837e-05 |
| 1,178 | Counting and Sampling Triangles from a Graph Stream | 2013 | VLDB | 0.00011907399 |
| 4,930 | Better Algorithms for Counting Triangles in Data Streams | 2016 | PODS | 6.5040855e-05 |
| 11,323 | Approximately Counting Subgraphs in Data Streams | 2022 | PODS | 5.1725247e-05 |
| 4,018 | Efficient Bi-triangle Counting for Large Bipartite Networks | 2021 | VLDB | 7.0241264e-05 |
| 9,241 | Efficiently Counting Triangles in Large Temporal Graphs | 2025 | SIGMOD | 5.3572577e-05 |
| 6,619 | Triangle and Four Cycle Counting in the Data Stream Model | 2020 | PODS | 5.8801548e-05 |
| 6,236 | The Complexity of Counting Cycles in the Adjacency List Streaming Model | 2019 | PODS | 6.0070757e-05 |