Near-Optimal Four-Cycle Counting in Graph Streams
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917377409548288 |
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| author | Lüderssen, Sebastian Neumann, Stefan Peng, Pan |
| author_facet | Lüderssen, Sebastian Neumann, Stefan Peng, Pan |
| contents | We study four-cycle counting in arbitrary order graph streams. We present a 3-pass algorithm for $(1+\varepsilon)$-approximating the number of four-cycles using $\widetilde{O}(m/\sqrt{T})$ space, where $m$ is the number of edges and $T$ the number of four-cycles in the graph. This improves upon a 3-pass algorithm by Vorotnikova using space $\widetilde{O}(m/T^{1/3})$ and matches a multi-pass lower bound of $Ω(m/\sqrt{T})$ by McGregor and Vorotnikova. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00828 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Near-Optimal Four-Cycle Counting in Graph Streams Lüderssen, Sebastian Neumann, Stefan Peng, Pan Data Structures and Algorithms We study four-cycle counting in arbitrary order graph streams. We present a 3-pass algorithm for $(1+\varepsilon)$-approximating the number of four-cycles using $\widetilde{O}(m/\sqrt{T})$ space, where $m$ is the number of edges and $T$ the number of four-cycles in the graph. This improves upon a 3-pass algorithm by Vorotnikova using space $\widetilde{O}(m/T^{1/3})$ and matches a multi-pass lower bound of $Ω(m/\sqrt{T})$ by McGregor and Vorotnikova. |
| title | Near-Optimal Four-Cycle Counting in Graph Streams |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2604.00828 |