Balls into bins via local search: cover time and maximum load
We study a natural process for allocating m balls into n bins that are organized as the vertices of an undirected graph G. Balls arrive one at a time. When a ball arrives, it 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. Then the next ball arrives and this procedure is repeated. For the case m=n, we give an upper bound for the maximum load on graphs with bounded degrees. We also propose the study of the cover time of this process, which is defined as the smallest m so that every bin has at least one ball allocated to it. We establish an upper bound for the cover time on graphs with bounded degrees. Our bounds for the maximum load and the cover time are tight when the graph is vertex transitive or sufficiently homogeneous. We also give upper bounds for the maximum load when m>=n.
Balls and Bins
Stochastic Process
Randomized Algorithm
187-198
Regular Paper
Karl
Bringmann
Karl Bringmann
Thomas
Sauerwald
Thomas Sauerwald
Alexandre
Stauffer
Alexandre Stauffer
He
Sun
He Sun
10.4230/LIPIcs.STACS.2014.187
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode