Efficient Load-Balancing through Distributed Token Dropping

We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and more generally for locally optimal semi-matchings. The prior work by Czygrinow et al. (DISC 2012) finds a stable orientation in $O(Δ^5)$ rounds in graphs of maximum degree $Δ$, while we improve it to $O(Δ^4)$ and also prove a lower bound of $Ω(Δ)$.