# Deterministic Distributed Vertex Coloring: Simpler, Faster, and without Network Decomposition

@article{Ghaffari2022DeterministicDV, title={Deterministic Distributed Vertex Coloring: Simpler, Faster, and without Network Decomposition}, author={Mohsen Ghaffari and Fabian Kuhn}, journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)}, year={2022}, pages={1009-1020} }

We present a simple deterministic distributed algorithm that computes a ($\Delta+1$)-vertex coloring in $O(\text{log}^{2}\Delta. \text{log}\ n)$ rounds. The algorithm can be implemented with $O(\text{log}\ n)$-bit messages. The algorithm can also be extended to the more general ($degree+1$)-list coloring problem. Obtaining a polylogarithmic-time deterministic algorithm for ($\Delta +1$)-vertex coloring had remained a central open question in the area of distributed graph algorithms since the…

## 23 Citations

### Distributed Graph Coloring Made Easy

- Computer ScienceSPAA
- 2021

A deterministic CONGEST algorithm to compute an O(kΔ)-vertex coloring in O( Δ/k)+łog^* n rounds, where Δ is the maximum degree of the network graph and 1łeq kłeq O(Δ) can be freely chosen.

### Locally-iterative $(\Delta+1)$-Coloring in Sublinear (in $\Delta$) Rounds

- Computer Science, Mathematics
- 2022

This paper gives the first locally-iterative (∆ + 1) -coloring algorithm with sublinear-in- ∆ running time, and answers the main open question raised in a recent breakthrough.

### Distributed $\Delta$-Coloring Plays Hide-and-Seek

- Computer Science, Mathematics
- 2021

Lower bounds as a function of ∆ are proved for a large class of distributed symmetry breaking problems, which can all be solved by a simple sequential greedy algorithm.

### Near-optimal distributed degree+1 coloring

- Computer ScienceSTOC
- 2022

A randomized distributed algorithm for D1LC that is optimal under plausible assumptions about the deterministic complexity of the problem is given, matching the best bound known for (Δ+1)-coloring.

### Distributed Edge Coloring in Time Polylogarithmic in $\Delta$

- Computer Science
- 2022

It is shown that a (2∆ − 1)-edge coloring can be computed in time poly log ∆+ O (log ∗ n ) in the LOCAL model, which improves a result of Balliu, Kuhn, and Olivetti [PODC ’20], who gave an algorithm with a quasi-polylogarithmic dependency on ∆.

### Distributed Edge Coloring in Time Polylogarithmic in Δ

- Computer SciencePODC
- 2022

It is shown that a (2Δ - 1)-edge coloring can be computed in time poly log Δ + O(log* n) in the LOCAL model, which improves a result of Balliu, Kuhn, and Olivetti [PODC '20], who gave an algorithm with a quasi-polylogarithmic dependency on Δ.

### Deterministic graph coloring in the streaming model

- Computer Science, MathematicsSTOC
- 2022

It is proved that there is no deterministic single-pass semi-streaming algorithm that given a graph G with maximum degree Δ, can output a proper coloring of G using any number of colors which is sub-exponential in Δ.

### Ultrafast Distributed Coloring of High Degree Graphs

- Computer ScienceArXiv
- 2021

A new randomized distributed algorithm that can color all n-node graphs of maximum degree ∆ ≥ log n in O(log∗ n) rounds and shows that the randomized complexity of ∆ + 1-list coloring in Congest depends inherently on the deterministic complexity of related coloring problems.

### Fast Distributed Vertex Splitting with Applications

- Mathematics, Computer Science
- 2022

A randomized poly log log n -round CONGEST algorithm for (1 + ε )∆ -edge coloring n -node graphs of suﬃciently large constant maximum degree ∆, for any ε > 0 .

### Improved Deterministic (Δ+1) Coloring in Low-Space MPC

- Computer Science, MathematicsPODC
- 2021

The Chang-Li-Pettie algorithm runs in T_local =poly(loglog n) rounds, which sets the state-of-the-art randomized round complexity for the problem in the local model, and employs a combination of tools, notably pseudorandom generators (PRG) and bounded-independence hash functions.

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