Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, April 14, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Daniel Bertschinger

An Optimal Decentralized (Δ + 1)-Coloring Algorithm

Consider the following simple coloring algorithm for a graph on n vertices. Each vertex chooses a color from {1,..., Δ + 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]. This is joint work with J. Lengler, A. Martinsson, R. Meier, A. Steger, M. Trujic, and E. Welzl.

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