License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2014.187
URN: urn:nbn:de:0030-drops-44570
URL: https://drops.dagstuhl.de/opus/volltexte/2014/4457/
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Bringmann, Karl ; Sauerwald, Thomas ; Stauffer, Alexandre ; Sun, He

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

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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.

BibTeX - Entry

@InProceedings{bringmann_et_al:LIPIcs:2014:4457,
  author =	{Karl Bringmann and Thomas Sauerwald and Alexandre Stauffer and He Sun},
  title =	{{Balls into bins via local search: cover time and maximum load}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{187--198},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Ernst W. Mayr and Natacha Portier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4457},
  URN =		{urn:nbn:de:0030-drops-44570},
  doi =		{10.4230/LIPIcs.STACS.2014.187},
  annote =	{Keywords: Balls and Bins, Stochastic Process, Randomized Algorithm}
}

Keywords: Balls and Bins, Stochastic Process, Randomized Algorithm
Collection: 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)
Issue Date: 2014
Date of publication: 05.03.2014


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