迁移受限的单机联机负载均衡
Online Load Balancing on Uniform Machines with Limited Migration
摘要：
在具有有限迁移的均匀相关机器上的在线负载均衡问题中，作业一个接一个地到达在线，并且必须立即被放置在给定的机器集合中的一台机器上，而不知道稍后可能到达的作业。每个作业有一个大小，每个机器有一个速度，分配给机器的作业的负载通过将第一个值除以第二个值来获得。目标是最小化任何机器接收的最大总负载。然而，与纯粹的在线情况不同，每次新工作的到来，它所带来的迁移潜力等于其规模和某个迁移系数的乘积。可以立即（非摊销情况）或在以后的任何时间（摊销情况）花费该潜力来重新分配作业。这种风格的半在线模型已经被深入研究了几个基本问题，例如，相同机器上的负载均衡和装箱，但到目前为止还没有考虑到均匀相关的机器。本文将均匀相关机器上的经典加倍策略与迁移相结合，分别实现了$(8/3+\varepsilon)$ -竞争算法和具有$O(1/\varepsilon)$摊销迁移和非摊销迁移的$(4+\varepsilon)$ -竞争算法，而在纯在线环境下已知的最佳竞争比大致为$5.828$ .
英文摘要：
In the problem of online load balancing on uniformly related machines with bounded migration, jobs arrive online one after another and have to be immediately placed on one of a given set of machines without knowledge about jobs that may arrive later on. Each job has a size and each machine has a speed, and the load due to a job assigned to a machine is obtained by dividing the first value by the second. The goal is to minimize the maximum overall load any machine receives. However, unlike in the pure online case, each time a new job arrives it contributes a migration potential equal to the product of its size and a certain migration factor. This potential can be spend to reassign jobs either right away (non-amortized case) or at any later time (amortized case). Semi-online models of this flavor have been studied intensively for several fundamental problems, e.g., load balancing on identical machines and bin packing, but uniformly related machines have not been considered up to now. In the present paper, the classical doubling strategy on uniformly related machines is combined with migration to achieve an $(8/3+\varepsilon)$-competitive algorithm and a $(4+\varepsilon)$-competitive algorithm with $O(1/\varepsilon)$ amortized and non-amortized migration, respectively, while the best known competitive ratio in the pure online setting is roughly $5.828$.
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。
