最佳球回收
Optimal Ball Recycling
摘要：
球和箱子游戏是一个非常成功的建模负载均衡问题的工具。在本文中，我们研究了一个新的场景，我们称之为球回收游戏，定义如下：把m个球扔到n个箱子里。然后，在每个时间步，选择一个非空的箱子并回收它的球：从选定的箱子中取出球，并根据p重新投掷它们。我们的目标是有一个捡箱方法，最大限度地提高回收率，定义为预期数量的球回收每一步的固定分布。我们研究了两个自然的策略球回收：满箱，其中greenetly挑选箱子的最大数量的球，和随机球，随机挑选一个球，并回收它的箱子。我们发现，对于一般的p，随机球是恒定的最优，而满斌可以是悲观的。然而，当p = u时，均匀分布，最满箱在加性常数内是最佳的。
英文摘要：
Balls-and-bins games have been a wildly successful tool for modeling load balancing problems. In this paper, we study a new scenario, which we call the ball recycling game, defined as follows: Throw m balls into n bins i.i.d. according to a given probability distribution p. Then, at each time step, pick a non-empty bin and recycle its balls: take the balls from the selected bin and re-throw them according to p. This balls-and-bins game closely models memory-access heuristics in databases. The goal is to have a bin-picking method that maximizes the recycling rate, defined to be the expected number of balls recycled per step in the stationary distribution. We study two natural strategies for ball recycling: Fullest Bin, which greedily picks the bin with the maximum number of balls, and Random Ball, which picks a ball at random and recycles its bin. We show that for general p, Random Ball is constant-optimal, whereas Fullest Bin can be pessimal. However, when p = u, the uniform distribution, Fullest Bin is optimal to within an additive constant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
