| Autor: |
Bertschinger, Daniel, Lengler, Johannes, Martinsson, Anders, Meier, Robert, Steger, Angelika, Trujić, Miloš, Welzl, Emo |
| Rok vydání: |
2020 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
Consider the following simple coloring algorithm for a graph on $n$ vertices. Each vertex chooses a color from $\{1, \dotsc, \Delta(G) + 1\}$ uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at random and recolor it with a randomly chosen color. This algorithm was introduced by Bhartia et al. [MOBIHOC'16] for channel selection in WIFI-networks. We show that this algorithm always converges to a proper coloring in expected $O(n \log \Delta)$ steps, which is optimal and proves a conjecture of Chakrabarty and Supinski [SOSA'20]. |
| Databáze: |
arXiv |
| Externí odkaz: |
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