AI 中文总结
研究随机负载均衡新变体，通过分两阶段（先k预留，后一致分配）解决问题，在相同机器设置下2预留可实现常数因子近似，还给出相关机器设置下的多种算法近似结果。
AI 中文摘要
我们引入了一种新型的随机负载均衡变体，它能在非自适应策略的实际好处与其性能限制之间进行定量权衡。我们的模型分两个阶段描述解决方案。第一阶段，仅根据作业大小分布，为每个作业预留至多k台机器（k预留）。第二阶段，在观察到作业大小实现后，将每个作业分配到其预留机器之一（一致分配），目标是最小化期望完工时间。若k = 1，得到标准随机负载均衡问题；若k等于机器数量，则得到全知最优。我们给出了一些量化这种权衡的结果。最显著的是，在相同机器设置下，2预留足以实现全知最优的常数因子近似；在相关机器设置下情况不同，但也给出了一些积极算法结果，如真正的O(log m/log log m)近似等。
英文摘要
We introduce a novel variant of stochastic load balancing that enables a quantitative tradeoff between the practical benefits of non-adaptive policies and their performance limitations. Our model describes a solution in two stages. In the first stage, given only job-size distributions, we reserve a set of at most k machines for each job (a k-reservation). In the second stage, after observing job-size realizations, we assign each job to one of its reserved machines (a consistent assignment). The goal is to minimize the expected makespan. If k=1, we get the standard stochastic load balancing problem of finding a non-adaptive assignment with minimum expected makespan. If k is equal to the number of machines, then we obtain an all-powerful omniscient optimum that can tailor the assignment arbitrarily to the job-size realizations. We give a number of results that quantify this tradeoff. Most saliently, we show that in the setting of identical machines, a 2-reservation suffices to achieve a constant-factor approximation to the omniscient optimum, establishing a "power-of-two-choices" result for stochastic load balancing. We also show that this no longer holds true in the more challenging setting of related machines. Nonetheless, we give a number of positive algorithmic results for this setting: a true O(log m/log log m)-approximation; a bicriteria O(1)-approximation by reserving twice as many machines per job relative to an optimal k-reservation; and a 2-reservation whose cost is within a constant factor of what the adaptive optimum can achieve.
Comments37 pages. Preliminary version appeared at IPCO 2026
