AI 中文总结
该研究针对双选择球入桶的广义问题，证明贪心算法对凸凹函数可获最优摊销界，还提出无摊销的非平凡界算法，并将其应用于不相关机器完成时间最小化的随机模型，设计出竞争性算法。
AI 中文摘要
考虑一组桶和服从泊松过程到达的双选择球，我们必须将每个到达的球立即分配到两个关联桶中的一个。对于给定函数$f$及每个桶，我们旨在基于关联到该桶的球的到达率，对$f(L)$的期望进行界定，其中$L$为该桶的最终负载。我们将此问题称为广义球入桶问题，它涵盖了诸多问题作为特例，包括Azar等人1994年提出的原始球入桶问题，以及Feldman等人2009年提出的在线随机匹配问题。我们证明，贪心算法对所有凸函数和凹函数$f$都能提供最优的摊销界。此外，我们提出了另一种算法，该算法无需摊销即可实现非平凡的界。作为应用，我们针对不相关机器上的完成时间最小化随机模型设计了一种竞争性算法。
英文摘要
Consider a set of bins and two-choice balls arriving by a Poisson process. We must allocate each incoming ball immediately to one of two incident bins. For a given function $f$ and every bin, we aim to bound the expectation of $f(L)$---where $L$ is the bin's final load---based on the arrival rate of balls incident to that bin. We call this problem Generalized Balls into Bins, capturing many problems as special cases including the original Balls into Bins by Azar et al. (1994) and Online Stochastic Matching by Feldman et al. (2009). We show that Greedy provides optimal amortized bounds for all convex and concave functions $f$. Further, we propose another algorithm that achieves non-trivial bounds without amortization. As an application, we design a competitive algorithm for a stochastic model of completion time minimization on unrelated machines.
