A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929432911937536 |
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| author | Dhawan, Abhishek |
| author_facet | Dhawan, Abhishek |
| contents | We present a simple $(1+\varepsilon)Δ$-edge-coloring algorithm for graphs of maximum degree $Δ= Ω(\log n / \varepsilon)$ with running time $O\left(m\,\log^3 n/\varepsilon^3\right)$. Our algorithm improves upon that of [Duan, He, and Zhang; SODA19], which was the first near-linear time algorithm for this problem. While our results are weaker than the current state-of-the-art, our approach is significantly simpler, both in terms of analysis as well as implementation, and may be of practical interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time Dhawan, Abhishek Data Structures and Algorithms Combinatorics We present a simple $(1+\varepsilon)Δ$-edge-coloring algorithm for graphs of maximum degree $Δ= Ω(\log n / \varepsilon)$ with running time $O\left(m\,\log^3 n/\varepsilon^3\right)$. Our algorithm improves upon that of [Duan, He, and Zhang; SODA19], which was the first near-linear time algorithm for this problem. While our results are weaker than the current state-of-the-art, our approach is significantly simpler, both in terms of analysis as well as implementation, and may be of practical interest. |
| title | A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time |
| topic | Data Structures and Algorithms Combinatorics |
| url | https://arxiv.org/abs/2407.16585 |