A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time
A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time
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.
22 pages, 6 figures
- Georgia Institute of Technology United States
FOS: Computer and information sciences, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO)
FOS: Computer and information sciences, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO)
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