2020/02/12 by Daniel Bertschinger, Johannes Lengler, Bertschinger, Daniel +11
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Cooperative Communication and Network Coding #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2002.05121
openalex publication_date 2020/02/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Consider the following simple coloring algorithm for a graph on n vertices. Each vertex chooses a color from \1, \dotsc, Δ(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 Δ) steps, which is optimal and proves a conjecture of Chakrabarty and Supinski [SOSA'20].