机器最小化的在线算法
Online Algorithms for Machine Minimization
摘要：
在本文中，我们考虑机器最小化问题的在线版本（由Chuzhoy等人介绍，FOCS 2004），其目标是在最少数量的相同机器上调度一组具有发布时间、截止日期和处理长度的作业。由于在线问题具有强下界，如果所有的工作参数是任意的，我们专注于统一长度的工作。我们的主要结果是一个完整的解决方案，这个问题的确定性的复杂性表明，竞争比$e$是可实现的和最佳的，从而提高现有的下限和上限分别为2.09和5.2。我们还给出了一个恒定的竞争力的在线算法的情况下，统一的最后期限（但任意的工作长度），据我们所知，没有这样的算法是已知的。最后，我们考虑了吞吐量最大化的互补问题，其目标是最大化一组固定的相同机器上的预定作业的权重之和（由Bar-Noy等STOC 1999年引入）。我们给出了一个随机在线算法，这个问题的竞争比的E/E-1，以前的结果实现了这一界的情况下，一台机器或在一个无限数量的机器的限制。
英文摘要：
In this paper, we consider the online version of the machine minimization problem (introduced by Chuzhoy et al., FOCS 2004), where the goal is to schedule a set of jobs with release times, deadlines, and processing lengths on a minimum number of identical machines. Since the online problem has strong lower bounds if all the job parameters are arbitrary, we focus on jobs with uniform length. Our main result is a complete resolution of the deterministic complexity of this problem by showing that a competitive ratio of $e$ is achievable and optimal, thereby improving upon existing lower and upper bounds of 2.09 and 5.2 respectively. We also give a constant-competitive online algorithm for the case of uniform deadlines (but arbitrary job lengths); to the best of our knowledge, no such algorithm was known previously. Finally, we consider the complimentary problem of throughput maximization where the goal is to maximize the sum of weights of scheduled jobs on a fixed set of identical machines (introduced by Bar-Noy et al. STOC 1999). We give a randomized online algorithm for this problem with a competitive ratio of e/e-1; previous results achieved this bound only for the case of a single machine or in the limit of an infinite number of machines.
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。
