Canonization of a random graph by two matrix-vector multiplications
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911761616076800 |
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| author | Verbitsky, Oleg Zhukovskii, Maksim |
| author_facet | Verbitsky, Oleg Zhukovskii, Maksim |
| contents | We show that a canonical labeling of a random $n$-vertex graph can be obtained by assigning to each vertex $x$ the triple $(w_1(x),w_2(x),w_3(x))$, where $w_k(x)$ is the number of walks of length $k$ starting from $x$. This takes time $O(n^2)$, where $n^2$ is the input size, by using just two matrix-vector multiplications. The linear-time canonization of a random graph is the classical result of Babai, Erdős, and Selkow. For this purpose they use the well-known combinatorial color refinement procedure, and we make a comparative analysis of the two algorithmic approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03686 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Canonization of a random graph by two matrix-vector multiplications Verbitsky, Oleg Zhukovskii, Maksim Computational Complexity We show that a canonical labeling of a random $n$-vertex graph can be obtained by assigning to each vertex $x$ the triple $(w_1(x),w_2(x),w_3(x))$, where $w_k(x)$ is the number of walks of length $k$ starting from $x$. This takes time $O(n^2)$, where $n^2$ is the input size, by using just two matrix-vector multiplications. The linear-time canonization of a random graph is the classical result of Babai, Erdős, and Selkow. For this purpose they use the well-known combinatorial color refinement procedure, and we make a comparative analysis of the two algorithmic approaches. |
| title | Canonization of a random graph by two matrix-vector multiplications |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2312.03686 |