# 2009, English, Article edition: A Note on Node Coloring in the SINR Model Derbel, Bilel; Mahmoud, Hammouda; Talbi, El-Ghazali

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Bookmark: http://trove.nla.gov.au/version/202377
Physical Description
• text
Published
• HAL - CCSD
• 2009
Language
• English

### Edition details

Title
• A Note on Node Coloring in the SINR Model
Author
• Derbel, Bilel
• Mahmoud, Hammouda
• Talbi, El-Ghazali
Published
• HAL - CCSD
• 2009
Physical Description
• text
Subjects
Notes
• 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.
• HAL:inria-00408670, version 1
• HAL:http:/​/​hal.inria.fr/​inria-00408670/​en/​
Language
• English
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