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# A Note on Node Coloring in the SINR Model

* Corresponding author
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : A $\xi$-coloring of a graph $G$ is a coloring of the nodes of $G$ with $\xi$ colors in such a way any two neighboring nodes have different colors. We prove that there exists a $O(\Delta \log n)$ time distributed algorithm computing a $O(\Delta)$-colroing for unit disc graphs under the signal-to-interference-plus-noise ratio (SINR)-based physical model ($\Delta$ is the maximum degree of the graph). We also show that, for a well defined constant $d$, a $d$-hop $O(\Delta)$-coloring allows us to schedule an interference free MAC protocol under the physical SINR constraints. For instance this allows us to prove that any point-to-point message passing algorithm with running time $\tau$ can be simulated in the SINR model in $O(\Delta (\log n + \tau))$ time using messages of well chosen size. All our algorithms are proved to be correct with high probability.
Document type :
Reports (Research report)

Cited literature [9 references]

https://hal.inria.fr/inria-00408670
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Submitted on : Thursday, October 22, 2009 - 2:11:16 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:12 AM
Long-term archiving on: : Friday, September 24, 2010 - 11:21:54 AM

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RR-7058.pdf
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### Identifiers

• HAL Id : inria-00408670, version 4

### Citation

Bilel Derbel, El-Ghazali Talbi. A Note on Node Coloring in the SINR Model. [Research Report] RR-7058, INRIA. 2009, pp.15. ⟨inria-00408670v4⟩

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