文章基本信息

标题：Balls into bins via local search: cover time and maximum load
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作者：Karl Bringmann ; Thomas Sauerwald ; Alexandre Stauffer 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2014
卷号：25
页码：187-198
DOI：10.4230/LIPIcs.STACS.2014.187
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Balls and Bins; Stochastic Process; Randomized Algorithm