Efficient Load-Balancing through Distributed Token Dropping

Summary

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). For the more general problem of locally optimal semi-matchings, the prior upper bound is O(S^5) and our new algorithm runs in O(C · S^4) rounds, which is an improvement for C = o(S); here C and S are the maximum degrees of customers and servers, respectively.