Efficient Load-Balancing through Distributed Token Dropping

TL;DR

This paper introduces the token dropping game as a new graph problem and leverages it to develop more efficient distributed algorithms for stable orientations and semi-matchings, improving previous round complexity bounds.

Contribution

It defines the token dropping game and applies it to design faster distributed algorithms for stable orientations and semi-matchings, reducing round complexity from prior work.

Findings

Improved distributed algorithm for stable orientations to O(Δ^4) rounds.

Proved a lower bound of Ω(Δ) rounds for the problem.

Introduced the token dropping game as a novel tool for distributed graph algorithms.

Abstract

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 $O(\Delta^5)$ rounds in graphs of maximum degree $\Delta$, while we improve it to $O(\Delta^4)$ and also prove a lower bound of $\Omega(\Delta)$.