Ultra-Fast Load Balancing on Scale-Free Networks

The performance of large distributed systems crucially depends on efficiently balancing their load. This has motivated a large amount of theoretical research how an imbalanced load vector can be smoothed with local algorithms. For technical reasons, the vast majority of previous work focuses on regular (or almost regular) graphs including symmetric topologies such as grids and hypercubes, and ignores the fact that large networks are often highly heterogenous. We model large scale-free networks by Chung-Lu random graphs and analyze a simple local algorithm for iterative load balancing. On n-node graphs our distributed algorithm balances the load within O((log logn)) steps. It does not need to know the exponent β ∈ (2, 3) of the power-law degree distribution or the weights wi of the graph model. To the best of our knowledge, this is the first result which shows that load-balancing can be done in double-logarithmic time on realistic graph classes.