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- W4232102009 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)The (1 + β)-Choice Process and Weighted Balls-into-BinsYuval Peres, Kunal Talwar, and Udi WiederYuval Peres, Kunal Talwar, and Udi Wiederpp.1613 - 1619Chapter DOI:https://doi.org/10.1137/1.9781611973075.131PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Suppose m balls are sequentially thrown into n bins where each ball goes into a random bin. It is well-known that the gap between the load of the most loaded bin and the average is , or large m. If each ball goes to the lesser loaded of two random bins, this gap dramatically reduces to Θ(log log n) independent of m. Consider now the following “(1 + β)-choice” process for some parameter β ∊ (0, 1): each ball goes to a random bin with probability (1 – β) and the lesser loaded of two random bins with probability β. How does the gap for such a process behave? Suppose that the weight of each ball was drawn from a geometric distribution. How is the gap (now defined in terms of weight) affected? In this work, we develop general techniques for analyzing such balls-into-bins processes. Specifically, we show that for the (1 + β)-choice process above, the gap is Θ(log n/β), irrespective of m. Moreover the gap stays at Θ(log n/β) in the weighted case for a large class of weight distributions. No non-trivial explicit bounds were previously known in the weighted case, even for the 2-choice paradigm. Previous chapter Next chapter RelatedDetails Published:2010ISBN:978-0-89871-701-3eISBN:978-1-61197-307-5 https://doi.org/10.1137/1.9781611973075Book Series Name:ProceedingsBook Code:PR135Book Pages:xviii + 1667" @default.
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- W4232102009 title "The (1 + β)-Choice Process and Weighted Balls-into-Bins" @default.
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