Balls into Bins via Local Search
Abstract
We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, where the ball is finally placed on. In our main result, we prove that this process yields a maximum load of only \Theta(\log \log n) on expander graphs. In addition, we show that for d-dimensional grids the maximum load is \Theta\Big(\big(\frac{\log n}{\log \log n}\big)^{\frac{1}{d+1}}\Big). Finally, for almost regular graphs with minimum degree \Omega(\log n), we prove that the maximum load is constant and also reveal a fundamental difference between random and arbitrary tie-breaking rules.
Keywords
Cite
@article{arxiv.1207.2125,
title = {Balls into Bins via Local Search},
author = {Paul Bogdan and Thomas Sauerwald and Alexandre Stauffer and He Sun},
journal= {arXiv preprint arXiv:1207.2125},
year = {2012}
}