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 Θ(log log n) on expander graphs. In addition, we show that for d-dimensional grids the maximum load is Θ(((log n)/(log log n))(1/(d+1))). Finally, for almost regular graphs with minimum degree Ω(log n), we prove that the maximum load is constant and also reveal a fundamental difference between random and arbitrary tie-breaking rules.
Original language | English |
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Title of host publication | Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, New Orleans, Louisiana, USA, January 6-8, 2013 |
Pages | 16-34 |
Number of pages | 19 |
ISBN (Electronic) | 978-1-61197-310-5 |
DOIs | |
Publication status | Published - 2013 |
Event | Twenty-Fourth Annual ASM-SIAM Symposium on Discrete Algorithms - Astor Crowne Plaza Hotel, New Orleans, United States Duration: 6 Jan 2013 → 8 Jan 2013 http://www.siam.org/meetings/da13/index.php |
Conference
Conference | Twenty-Fourth Annual ASM-SIAM Symposium on Discrete Algorithms |
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Abbreviated title | SODA 2013 |
Country/Territory | United States |
City | New Orleans |
Period | 6/01/13 → 8/01/13 |
Internet address |