# Local Conflict Coloring Revisited: Linial for Lists

@inproceedings{Maus2020LocalCC, title={Local Conflict Coloring Revisited: Linial for Lists}, author={Yannic Maus and Tigran Tonoyan}, booktitle={DISC}, year={2020} }

Linial's famous color reduction algorithm reduces a given $m$-coloring of a graph with maximum degree $\Delta$ to a $O(\Delta^2\log m)$-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to choose their color from a list of allowed colors: given an $m$-coloring in a directed graph of maximum outdegree $\beta$, if every node has a list of size $\Omega(\beta^2 (\log \beta+\log\log m + \log \log |\mathcal{C}|))$ from a color space $\mathcal{C}$ then…

## 13 Citations

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

- Computer Science2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
- 2022

An improved deterministic algorithm based on an improved variant of the network decomposition of Rozhoň and Ghaffari leads to an improvement in the complexity of randomized algorithms for ($\Delta +1$)-coloring, now reaching the bound of $O(\text{log}^{3}\text{ log}\ n)$ rounds.

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.

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 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.

Distributed ∆-coloring plays hide-and-seek

- Computer Science, MathematicsSTOC
- 2022

Lower bounds as a function of Δ are proved for a large class of distributed symmetry breaking problems, which can all be solved by a simple sequential greedy algorithm, including the maximal independent set (MIS) in trees.

Improved Distributed Fractional Coloring Algorithms

- Mathematics, Computer ScienceOPODIS
- 2021

The fractional coloring problem can be approximated arbitrarily well by an efficient algorithm in the LOCAL model, and it is shown that in regular grids of bounded dimension, a fractional (2 + ε )-coloring can be computed in time O (log ∗ n ).

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 ∆.

Efficient randomized distributed coloring in CONGEST

- Computer Science, MathematicsSTOC
- 2021

This work presents a new randomized distributed vertex coloring algorithm for the standard CONGEST model, where the network is modeled as an n-node graph G, and where the nodes of G operate in synchronous communication rounds in which they can exchange O(logn)-bit messages over all the edges of G.

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.

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.

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