Repository logo
 

Balls into bins via local search: Cover time and maximum load

Accepted version
Peer-reviewed

Loading...
Thumbnail Image

Type

Article

Change log

Authors

Bringmann, K 
Sauerwald, T 
Stauffer, A 
Sun, H 

Abstract

© 2015 Wiley Periodicals, Inc. Abstract-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.

Description

Keywords

balls-into-bins, load balancing, stochastic process, local search

Journal Title

Random Structures and Algorithms

Conference Name

Journal ISSN

1042-9832
1098-2418

Volume Title

48

Publisher

Wiley
Sponsorship
ETH Zurich Postdoctoral Fellowship Program Marie Curie Career Integration. Grant Number: PCIG13‐GA‐2013‐618588 DSRELIS