Online Interval Scheduling to Maximize Total Satisfaction, Theoretical Computer Science
Online Interval Scheduling to Maximize Total Satisfaction, Theoretical Computer Science
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在线间隔调度以最大化总体满意度，理论计算机科学
DOI：
10.1016/j.tcs.2019.10.046
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发表时间：
2020
影响因子：
1.1
通讯作者：
Koji M. Kobayashi
中科院分区：
文献类型：
--
作者：
松本麻衣;畑本陽一 ;村山知聡;坂本梓;池本真二;Koji M. Kobayashi
区间排序问题是排序问题的一个变种。本文提出了一种新的区间排序问题的变形，其定义如下：给定的工件由它们的释放时间，截止期和利润来指定。算法必须在m台相同机器中的一台机器上开始作业的发布时间，并继续处理，直到机器上的最后期限完成作业。所有的作业都必须完成，算法可以获得完成作业的利润作为用户的满意度。在一台机器上一次处理多个作业是可能的。一个工件的利润均匀分布在其发布时间和截止时间之间，即其间隔，从工件的子间隔获得的利润与同一机器上的间隔与子间隔相交的工件数量成反比。我们变量的目标是最大化已完成工作的总利润。这种提法自然是出于在许多情况下出现的尽最大努力的要求和对要求的回应。在尽力而为的请求和响应中，用户可用资源的总量始终不变，并且资源与每个用户平等共享。我们研究这个问题的在线算法。具体来说，我们表明，对于利润的工作是任意的情况下，不存在一个算法的竞争比是有界的。然后，我们考虑的情况下，每个工作的利润等于它的长度，即，它的发布时间和截止日期之间的时间间隔。对于这种情况，我们证明了当m= 2和m≥ 3时，贪婪算法的竞争比分别至多为4/3和至多为3.此外，对于每个m≥ 2，我们证明了任何确定性算法的竞争比的下界。
The interval scheduling problem is one variant of the scheduling problem. In this paper, we propose a novel variant of the interval scheduling problem, whose definition is as follows: given jobs are specified by their release times, deadlines and profits. An algorithm must start a job at its release time on one of m identical machines, and continue processing until its deadline on the machine to complete the job. All the jobs must be completed and the algorithm can obtain the profit of a completed job as a user's satisfaction. It is possible to process more than one job at a time on one machine. The profit of a job is distributed uniformly between its release time and deadline, that is its interval, and the profit gained from a subinterval of a job decreases in reverse proportion to the number of jobs whose intervals intersect with the subinterval on the same machine. The objective of our variant is to maximize the total profit of completed jobs. This formulation is naturally motivated by best-effort requests and responses to them, which appear in many situations. In best-effort requests and responses, the total amount of available resources for users is always invariant and the resources are equally shared with every user. We study online algorithms for this problem. Specifically, we show that for the case where the profits of jobs are arbitrary, there does not exist an algorithm whose competitive ratio is bounded. Then, we consider the case in which the profit of each job is equal to its length, that is, the time interval between its release time and deadline. For this case, we prove that for m= 2 and m≥ 3, the competitive ratios of a greedy algorithm are at most 4/3 and at most 3, respectively. Also, for each m≥ 2, we show a lower bound on the competitive ratio of any deterministic algorithm.