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

Authors Karl Bringmann, Thomas Sauerwald, Alexandre Stauffer, He Sun



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LIPIcs.STACS.2014.187.pdf
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Karl Bringmann
Thomas Sauerwald
Alexandre Stauffer
He Sun

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Karl Bringmann, Thomas Sauerwald, Alexandre Stauffer, and He Sun. Balls into bins via local search: cover time and maximum load. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 187-198, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.STACS.2014.187

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.
Keywords
  • Balls and Bins
  • Stochastic Process
  • Randomized Algorithm

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